Geometry Theorems and Problems - Recent Additions (Page 7 of 15)

Circular Segment. Index.
Theorems and Problems. 

Geometry Problem 988.
Right Triangle, Cevians, Angles, 30 Degrees, Triple Angle.

Geometry Problem 987.
Triangle, Circumcircle, Incenter, Chord, Parallel, Circle, Tangent. GeoGebra, HTML5 Animation for Tablets (iPad, Nexus).

Geometry Problem 986.
Triangle, Median, Midpoint, Equal Angles, 45 Degrees.

Geometry Problem 985.
Circle, Radius, Perpendicular, Concentric Circles, Congruence, Triangle.

Geometry Problem 984.
Triangle, Circumcircle, Altitudes, Midpoint, Collinear Points.

Geometry Problem 983.
Regular Hexagon, A point and six triangles, Areas.

Geometry Problem 982.
Triangle, Excenters, Excentral Triangle, Circumcenter, Area, Hexagon.

Geometry Problem 981.
Triangle, Concurrent Cevians, Midpoints, Area, Hexagon.

Geometry Problems 971 - 980.
Equilateral Triangle, Rectangle, Circle, Parallel, Reflection, Concurrency, Paallelogram, Orthocenter, Circumcenter.

Geometry Problem 980.
Equilateral Triangle, Vertices, Three Parallel, Equal Circles, Construction.

Geometry Problem 979.
Triangle, Cevian, Angle Bisector, Concurrency, 90 Degrees, Perpendicular.

Geometry Problem 978.
Parallelogram, Diagonal, Transversal, Similarity, Metric Relations.

Geometry Problem 977.
Acute Triangle, Circumcenter, Orthocenter, Distance, Circumradius, Altitude, Metric Relations.

Geometry Problem 976.
Isosceles Right Triangle, 45 Degrees, Incenter, Angle Bisector, Hypotenuse.

Geometry Problem 975.
Isosceles Right Triangle, 45 Degrees, Angle Bisector, Hypotenuse.

Geometry Problem 974.
'Begonia Theorem', Cevian Triangle, Reflection of a point in a line, Concurrency of Lines. GeoGebra, HTML5 Animation for Tablets.

Geometry Problem 973.
Three Parallel, Square, Vertices, Distance Between Two Parallel Lines, Side, Metric Relations.

Geometry Problem 972.
Equilateral Triangle, Vertices, Three Parallel, Equal Circles, Perpendicular Bisector.

Geometry Problem 971.
Equilateral Triangle, Rectangle, Common Vertex, Sum of Right Triangles Areas.

Geometry Problem 970.
Equilateral Triangle, Circumcircle, Secant, Metric Relations.

Geometry Problem 969.
Equilateral Triangle, Rectangle, Common Vertex, Right Triangles Areas.

Geometry Problem 968.
Equilateral Triangle, Rectangle, Common Vertex, Midpoint.

Geometry Problem 967.
Three Equilateral Triangles, Midpoints. GeoGebra, HTML5 Animation for Tablets (iPad, Nexus).

Geometry Problem 966.
Triangle, Cevians, Midpoint, Circumcircle, Circle, Tangent Line, Collinear Points.

Geometry Problem 965.
Triangle, Cevians, Midpoint, Circumcircle, Circle, Tangent Line, Metric Relations.

Geometry Problem 964.
Right Triangle, Cevians, Angles, 10, 20, 30 Degrees.

Geometry Problem 963.
Right Triangle, 30-60-90 Degrees, Angle Bisectors, Metric Relations.

Geometry Problem 962.
Triangle, Two Cevians, Areas, Equal Products.

Geometry Problem 961.
Quadrilateral, Trisection, Sides, Sum of Areas.

Geometry Problem 960.
Quadrilateral, Trisection, Sides, Congruence, Similarity, Triangle.

Geometry Problem 959.
Triangle, Sides Ratio 4:1, Inradius, Exradius, Cevian, Mean Proportional, Geometric Mean, Metric Relations.

Geometry Problem 958.
Isosceles Triangle, Altitude, 45 Degrees, Perpendicular, Angle Bisector, Metric Relations.

Geometry Problem 957.
Equilateral Triangle, Inscribed Circle, Incircle, Circumscribed Circle, Circumcircle, Area, Circular Segment.

Geometry Problem 956.
Two Equilateral Triangles, Center, Collinear Points, Midpoint, Right Triangle, 30, 60, 90 Degrees.

Geometry Problem 955.
Quadrilateral, Triangle, Diagonals, Triangle, Angles, 30, 40, 60, 70 Degrees.

Geometry Problem 954.
Intersecting Circles, Secant, Common Chord, Cyclic Quadrilateral, Angle Bisector.

Geometry Problem 953.
Intersecting Circles, Secant, Common Chord, Cyclic Quadrilateral, Perpendicular.

Geometry Problem 952.
Triangle, Incenter, Circumcenter, Three Equal Circles, Tangent Line, Tangent Circles, Collinear Points.

Geometry Problem 951.
Intersecting Circles, Chord, Diameter, Parallel, Cyclic Quadrilateral, Concyclic Points.

Geometry Problem 950.
Intersecting Circles, Secant, Cyclic Quadrilateral, Concyclic Points.

Geometry Problem 949.
Intersecting Circles, Secant, Cyclic Quadrilateral, Concyclic Points.

Geometry Problem 948.
Intersecting Circles, Secant, Cyclic Quadrilateral, Concyclic Points.

Geometry Problem 947.
Triangle, Circumcircle, Angle Bisector, Chord, Arc, Parallel.

Geometry Problem 946.
Triangle, Quadrilateral, Area, Diagonal, Midpoint, Parallel.

Geometry Problems 891 - 900.
Triangle, Circle, Parallelogram, Trapezoid, Congruence, Similarity, Metric Relations, Incircle, Rectangle, Square

Geometry Problem 945.
Triangle, Concurrent Lines, Cevians, Perpendicular, Angle Bisector.

Geometry Problem 944.
Triangle, Orthocenter, Altitude, Perpendicular, 90 Degrees, Parallel Lines.

Geometry Problem 943.
Triangle, Incircle, Inscribed Circle, Tangency Points, Parallel, Metric Relations.

Geometry Problem 942.
Triangle, Circles, Circumcircle, Sagitta, Incircle, Excircle, Inradius, Exradius, Metric Relations.

Geometry Problem 941.
Circles Tangent Externally, Tangent, Secant, Proportion, Angle.

Geometry Problem 940.
Circle, Tangent, Secant, Chord, Parallel, Perpendicular, 90 Degrees, Midpoint.

Geometry Problem 939.
Circle, Tangent, Secant, Chord, Parallel, Midpoint.

Geometry Problem 938.
Cyclic Quadrilateral, Triangle, Circumcircle, Circles, Circumcenter, Circumradius, Distance, Metric Relations.

Geometry Problem 937.
Triangle, Circumcircle, Circles, Tangent, Sides, Midpoint.

Geometry Problem 936.
Circle, Semicircle, Diameter, Tangent, Radius, Chord, Metric Relations.

Geometry Problem 935.
Square, Circle, Center, Perpendicular, Metric Relations.

Geometry Problem 934.
Square, Circle, Center, Perpendicular, Metric Relations.

Geometry Problem 933.
Square, Center, Transversal, Perpendicular, Metric Relations, Congruence.

Geometry Problem 932.
Square, Midpoint, Diagonal, Ratio 3:1, Angle Measure, Congruence.

Geometry Problem 931.
Square, Circle, Semicircle, Diameter, Triangle, Angle, Metric Relations.

Dynamic Geometry: Exeter Point
Triangle, Median, Circumcircle, Concurrent Lines, Euler Line, GeoGebra, HTML5 Animation for Tablets.

Geometry Problem 930.
Acute Triangle, Altitudes, Circles, Diameter, Angle, Measure.

Geometry Problem 929.
Triangle, Orthocenter, Circumcircle, Reflection, Concurrency.

Geometry Problem 928.
Triangle, Midpoint, Median, Cevian, Concurrency, Area.

Geometry Problem 927.
Semicircle, Diameter, Radius, Equal Arcs, Chord, Congruence.

Geometry Problem 926.
Two Equilateral Triangles, Midpoint, Perpendicular, Metric Relations.

Geometry Problem 925.
Cyclic Quadrilateral, Diagonal, Circle, Angle Bisector, Parallel.

Geometry Problem 924.
Quadrilateral, Diagonal, Perpendicular, Circle, Tangent, Midpoint, Metric Relations.

Geometry Problem 923.
Quadrilateral, Quadrangle, Obtuse Angle, Triangle, Diagonal, Inequality, Length.

Geometry Problem 922.
Circle, Tangent Lines, Tangency Points, Chord, Secant, Harmonic Mean.

Geometry Problem 921.
Right Triangle, Circumcircle, Arc, Midpoint, Tangency Point, Incircle.

Geometry Problem 920.
Triangle, Angles, 10, 20 Degrees, Congruence.

Geometry Problem 919.
Rhombus, Triangle, Perpendicular, 90 Degrees, Congruence.

Geometry Problem 918.
Triangle, Incenter, Incircle, Angle Bisector, Perpendicular, Metric Relations.

Geometry Problem 917.
Triangle, Congruence, Midpoints, Angle Bisector, Perpendicular.

Geometry Problem 916.
Cyclic Quadrilateral, Three Circles, Diameter, Congruence.

Geometry Problem 915.
Triangle, Intersecting Circles, Concyclic Points, Cyclic Quadrilateral.

Geometry Problem 914.
Triangle, Orthocenter, Angle Bisector, Parallel Lines, Midpoint.

Geometry Problem 913.
Right Triangle, Double Angle, Triple Angle, Metric Relations.

Geometry Problem 912.
Right Triangle, Double Angle, Triple Angle, Perpendicular Lines.

Geometry Problem 911.
Right Triangle, Double Angle, Triple Angle, Concyclic Points, Cyclic Quadrilateral.

Geometry Problem 910.
Bicentric Quadrilateral, Distance between the Incenter and Circumcenter, Incircle, Circumcircle, Circumscribed, Inscribed, Circumradius.

Geometry Problem 909.
Bicentric Quadrilateral, Incircle, Circumcircle, Circumscribed, Inscribed, Tangent, Inradius, Distance.

Geometry Problem 908.
Bicentric Quadrilateral, Incircle, Circumcircle, Circumscribed, Inscribed, Tangent, Inradius.

Geometry Problem 907.
Bicentric Quadrilateral, Incircle, Circumcircle, Circumscribed, Inscribed, Tangent, Inradius.

Geometry Problem 906.
Bicentric Quadrilateral, Incircle, Circumcircle, Circumscribed, Inscribed, Perpendicular.

Geometry Problem 905: Lester Circle Theorem.

Geometry Problem 904: Second Fermat Point: Static diagram.
Second Fermat Point: Dynamic diagram.
Triangle, Equilateral triangles, Concurrent lines, GeoGebra, HTML5 Animation for Tablets (iPad, Nexus)

Geometry Problem 903: First Fermat Point.
 

Geometry Problems 881 - 890.
Triangle, Circle, Parallelogram, Trapezoid, Congruence, Similarity, Metric Relations, Incircle, Rectangle, Square

Static Diagram of problem 902
Dynamic Geometry Problem 902
Triangle, Four Squares, Center, Concurrent Lines. GeoGebra, HTML5 Animation for Tablets

Static Diagram of problem 901
Dynamic Geometry Problem 901
Intersecting Circles, Common External Tangent, Secant, Circumcircle, Concyclic Points, Cyclic Quadrilateral. GeoGebra, HTML5 Animation for Tablets

Geometry Problem 900
Intersecting Circles, Common External Tangent, Secant, Angle, Congruence.
GeoGebra, HTML5 Animation for Tablets

Geometry Problem 899
Intersecting Circles, Common External Tangent, Secant, Concyclic Points, Cyclic Quadrilateral. GeoGebra, HTML5 Animation for Tablets

Geometry Problem 898
Intersecting Circles, Common External Tangent, Secant, Circumcenter, Collinear Points.
GeoGebra, HTML5 Animation for Tablets

Geometry Problem 897
Intersecting Circles, Common External Tangent, Secant, Congruence.
GeoGebra, HTML5 Animation for Tablets

Geometry Problem 896
Triangle, Orthocenter, Midpoint, Median, Intersecting Circles, Diameter, Collinear Points.
GeoGebra, HTML5 Animation for Tablets

Geometry Problem 895
Triangle, Incircle, Tangency Points, Parallel line, Collinear Points.
GeoGebra, HTML5 Animation for Tablets

Geometry Problem 894
Triangle, Angle, 60 degrees, Incenter, Midpoint, Parallel Lines.
GeoGebra, HTML5 Animation for Tablets

Geometry Problem 893
Triangle, Circumcircle, Incenter, Circle, Tangent, Collinear Points.
GeoGebra, HTML5 Animation for Tablets

Geometry Problem 892
Triangle, 60 degrees, Orthocenter, Circumcenter.

Geometry Problem 891
Equiangular Octagon, Metric Relations, Sides, Auxiliary Lines.

Geometry Problem 890
Two Squares inscribed in Circles, Concurrent Lines. GeoGebra, HTML5 Animation for Tablets.

Geometry Problem 889
Carnot's Theorem in an acute triangle, Circumcenter, Circumradius, Inradius. GeoGebra, HTML5 Animation for Tablets.

Geometry Problems 871 - 880.
Triangle, Circle, Parallelogram, Trapezoid, Congruence, Similarity, Metric Relations, Incircle, Rectangle, Square

Geometry Problem 888
Butterfly Theorem, Circle, Chord, Midpoint. GeoGebra, HTML5 Animation for Tablets.

Geometry Problem 887
Triangle, Altitude, Angle Bisector, Perpendicular, Midpoint, Concyclic Points. GeoGebra, HTML5 Animation for Tablets.

Geometry Problem 886
Right Triangle, Incenter, Angle Bisector, Perpendicular, 45 Degrees, Concyclic Points, Isosceles Right Triangle. GeoGebra, HTML5 Animation for Tablets (iPad, Nexus)..

Geometry Problem 885
Intersecting Circles, Three Tangent Lines, Midpoint.

Geometry Problem 884: The Pythagorean Curiosity
Right Triangles and squares, fifteen conclusions.

Geometry Problem 883
Five Circumscribed Quadrilaterals, Circle, Tangent, Common Tangent.

Geometry Problem 882
Triangle, Angle x, 2x, 7x, Cevian, Congruence, Auxiliary Lines.

Geometry Problem 881
Triangle, three Squares, Centers, Areas.

Geometry Problem 880
Triangle, Midpoints, Sides, Perpendiculars, Hexagon, Area.

Geometry Problem 879
Square, Midpoint, Diagonal, Ratio 3:1, Angle Measure.

Geometry Problem 878
Square, Inscribed Circle, Quadrant, Center, Perpendicular, Metric Relations.

Geometry Problem 877
Square, Right Triangle, Similarity, Metric Relations, Transversal.

Geometry Problem 876
Equilateral Triangle, any Point, Perpendicular, Right Triangle Area, Sum of Areas.

Geometry Problem 875
Congruent Circles, Intersecting Circles, Secant, Center, Angle Trisection, Triple Angle.

Geometry Problem 874
Isosceles Triangle, Circumcircle, Circumcenter, Congruence.

Geometry Problem 873
Quadrilateral, Diagonal, Triangle, Angle Bisector, Congruence.

Geometry Problem 872
Quadrilateral, Triangle, Angle, 30, 90 degrees.

Cyclic Quadrilateral with Perpendicular Diagonals.

Geometry Problem 871
Brahmagupta's Theorem, Cyclic Quadrilateral, Perpendicular Diagonals, Midpoint.

Geometry Problem 870
Triangle, Median, Three Squares, Centers, Vertices, Collinear Points, Midpoint.

Geometry Problem 869
Triangle, Median, Three Equilateral Triangles, Collinear Points, Midpoint.

Geometry Problem 868
Cyclic Quadrilateral, Circle, Five Rectangles, Four Centers, Congruence.

GeoGebra, Dynamic Geometry: Internal Feuerbach Point
HTML5 Animation for Tablets (iPad, Nexus..)

Geometry Problem 867
Isosceles Triangle, Median, Perpendicular, Angle, Congruence.

Geometry Problem 866
Cyclic Quadrilateral, Circle, Rectangle, Center, Congruence, 90 Degrees.

Geometry Problem 865
Parallelogram, Diagonal, Midpoint, Side, Triangle, Parallel, Similarity.

Geometry Problem 864
Parallelogram, Diagonal, Congruence, Similarity, Metric Relations.

GeoGebra, Dynamic Geometry: Nine Point Circle
HTML5 Animation for Tablets (iPad, Nexus..)

GeoGebra, Dynamic Geometry: Lemoine Line of a Triangle.
HTML5 Animation for Tablets (iPad, Nexus..)

GeoGebra, Dynamic Geometry: Simson Line of a Triangle.
HTML5 Animation for Tablets (iPad, Nexus..)

GeoGebra, Dynamic Geometry: Euler Line of a Triangle.
HTML5 Animation for Tablets (iPad, Nexus..)

Geometry Problem 863
Circumscribed trapezoid, Inscribed Circle, Tangent, Metric Relations.

Geometry Problem 862:
Trapezoid, Parallel, Equal Areas, RMS, Root Mean Square
.

GeoGebra Constructions Index
HTML5 Animation for Tablets (iPad, Nexus..)

Geometry Problem 861
Triangle, Incircle, Parallel, Tangent, Metric Relations.

GeoGebra, Dynamic Geometry: Circumcenter and Circumcircle of a Triangle.
HTML5 Animation for Tablets (iPad, Nexus..)

GeoGebra, Dynamic Geometry: Centroid of a Triangle.
HTML5 Animation for Tablets (iPad, Nexus..)

GeoGebra, Dynamic Geometry: Incenter and Incircle of a Triangle.
HTML5 Animation for Tablets (iPad, Nexus..)

Root Mean Square (RMS) in Geometry Index

.

Geometry Art�Problems for Desktops, High-end mobile devices and Tablets (iPad, Nexus)
Visual Index.

GeoGebra, Dynamic Geometry: Orthocenter of a Triangle.
HTML5 Animation for Tablets (iPad, Nexus..)

Geometry Problem 860
Triangle, Three Medians, Parallel, Parallelogram, Area, Congruence.

Nine-Point Center, Nine-Point Circle, Euler Line. Interactive illustration.
Circumcenter, Centroid, Orthocenter
HTML5 Animation for iPad and Nexus

Lemoine Line Theorem, Interactive illustration.
HTML5 Animation for iPad and Nexus

Geometry Problem 859
Isosceles Right Triangle, Angles,18, 45 Degrees, Congruence, Perpendicular bisector.

Gergonne Point Theorem. Concurrency. Interactive proof with animation.
HTML5 Animation for Tablets (iPad, Nexus)
Adobe Flash Animation

Geometry Problem 858
Isosceles Right Triangle, Cevian, Ratio 2:1, 45 Degrees, Congruence, Angles, Auxiliary Lines.

Geometry Problem 857
Triangle, Median, Midpoint, Angles, 30, 45 Degrees, Congruence, Auxiliary Lines.

Geometry Problem 856
Quadrilateral, Diagonals, Triangle, Angles, 30 degrees, Congruence, Auxiliary lines.

Platonic Solids, Interactive animation.
HTML5 Animation for iPad and Nexus

Johnson's Theorem, Intersecting circles.
HTML5 Animation

Geometry Problem 855
Quadrilateral, Triangle, Angles, 30 degrees, Congruence, Auxiliary lines.

Geometry Problem 854
Triangle, Parallel lines, Parallelogram, Areas, Similarity, Concurrent lines.

Geometry Problem 853
Square, Arc, Quadrant, Triangle, Perpendicular, Metric Relations.

Geometry Problem 852
Triangle, Incircle, Inradius, Tangent, Metric Relations.

Geometry Problem 851
Triangle, Triple side, Angles, 90 Degrees, Special Right triangle, Sides ratio 1:3.

Geometry Problem 850
Triangle, Double side, Angles, 90 Degrees. Special Right triangle.

Geometry Problem 849
Special Right triangle, Catheti or legs ratio 1:3, 18.5 Degrees. Double angle.

Geometry Problem 848
Special Right triangle, Catheti or legs ratio 1:2, 26.5 Degrees. Double angle.

iPad Apps: Apollonius Software. Feuerbach Point. Triangle, Incircle, Nine point circle, Tangent circles, Orthocenter, Midpoint.
Interactive Geometry Software for iPad.

Geometry Designer for iPad, iPhone, iPod - Index
Dynamic Geometry.

Geometry Problem 847
van Lamoen Circle, Triangle, Medians, Centroid, Six Circumcenters, Concyclic Points.

iPad Apps, Geometry Designer Illustration. Circle of van Lamoen.
Interactive Geometry Software for iPad, iPhone, iPod.

iPad Apps: Geometry Designer Illustration. Four Circles Theorem.
Interactive Geometry Software for iPad, iPhone, iPod.

Geometry Problem 846
Triangle, Medians, Centroid, Four Circumcenters, Concyclic Points, Cyclic Quadrilateral, Similarity.

Geometry Problem 845
Triangle, Medians, Centroid, Four Circumcenters, Perpendicular,�Congruence, Similarity.

Geometry Problem 844
Triangle, Medians, Centroid, Four Circumcenters, Perpendicular,�Congruence, Similarity.

Geometry Problem 843
Triangle, Medians, Centroid, Four Circumcenters, Perpendicular,�Parallel, Congruence, Similarity.

Geometry Problem 842
Triangle, Medians, Centroid, Four Circumcenters, Perpendicular,�Congruence, Similarity.

Geometry Problem 841
Triangle, Medians, Centroid, Circumcenters, Perpendicular, Congruence, Similarity.

van Lamoen Circle - Index.

Geometry Problem 840
Parallelogram, Perpendicular, Diagonal, Metric Relations, Similarity.

Geometry Problem 839
Problem 839: Parallelogram, Perpendicular, Diagonal, Metric Relations.

Geometry Problem 838
Parallelogram, Perpendicular, Diagonal, Metric Relations.

Geometry Problem 837
Triangle, Orthocenter, Circumcenter, Circle, Concyclic Points.

Geometry Problem 836
Parallelogram, Perpendicular, Diagonal, Similarity, Metric Relations.

Geometry Problem 835
Isosceles Triangle, Double Angle, Triple Angle, Auxiliary Lines.

Prezi Presentation: A Geometry Course by Mark Vasicek
 

Geometry Problem 834
Parallelogram, Diagonal, Similarity, Geometric Mean, Mean Proportional.

Mean in Geometry.
Index.

Geometry Problem 833
Parallelogram, Diagonal, Similarity, Proportion.

Geometry Problem 832
Quadrilateral, Isosceles triangle, 70-70-40 degrees, Congruence, Auxiliary lines, Equilateral triangle.

Geometry Problem 831
Quadrilateral, Diagonal, Midpoint, Opposite Angles, Congruence, Parallelogram.

Geometry Problem 830
Quadrilateral, Triangle, Angles, 30 degrees, Congruence.

Geometry Problem 829
Triangle, Circumcircle, Parallel, Chord, Side, Metric Relations.

Geometry Problem 828
Quadrilateral, Midpoint, Opposite sides, Diagonals, Concurrent lines, Triangle, Bimedian.

Geometry Problem 827: Brianchon Corollary
Circumscribed Hexagon, Tangency Points, Diagonal, Opposite Sides, Concurrent lines.

Geometry Problem 826: Brianchon's Theorem
Circumscribed Hexagon, Concurrent Diagonals.

Geometry Problem 825.
Circle, Semicircle, Arc, Chord, Midpoint, Sector, Triangle, Area.

Geometry Problem 824
Desargues' Theorem, Triangles in Perspective.

Geometry Problem 823.
Tangent Circles, Diameter, Perpendicular, Chord, Secant, Triangle, Area, Tangency Point.

Circle Area. Index.
Theorems and Problems. 
 

Geometry Problem 822.
Circle, Semicircle, Arc, Chord, Midpoint, Sector, Triangle, Area.

Geometry Problem 821.
Adams Circle.

Geometry Problem 820.
Triangle, Cevian, Angles, 30 Degrees.

Geometry Problems 811 - 820.
Triangle, Circle, Quadrilateral, Square, Pitot Theorem, Arbelos, Tangent, 30 Degrees.

Geometry Problem 819.
Quadrilateral, Triangle, Angles, 30 degrees.

Geometry Problem 818.
Square, Triangle, Angle.

Geometry Problem 817.
Two circles, Tangent Lines, Circumscribed Quadrilaterals.

Geometry Problem 816.
Tangential or Circumscribed Quadrilateral: Pitot Theorem.

Geometry Problem 815.
Triangle, Incircle, Semicircles, Arbelos, Area.

Geometry Problem 814.
Two Equilateral Triangles with a common Vertex, Angle.

Geometry Problem 813.
Right Triangle Area, Excircles, Cathetus, Tangency Points, Quadrilateral Area.

Geometry Problem 812.
Four Tangent Circles, Common Tangent Line, Diameter, Area, Collinear Centers.

Geometry Problem 811: Trisecting a line segment.
With four circles and one line.

Geometry Problem 810: Trisecting a line segment.
With two circles and eight lines.

Geometry Problem 809: Trisecting a line segment.
With three circles and four lines.

Geometry Problem 808
Parallelogram, Perpendicular, Right Triangle, Semicircle Area, Diameter.

Geometry Problem 807
Right Triangle Area, Incircle, Tangency Points, Semicircle Area.

Lines. Theorems and Problems.

Trisecting a Line Segment.
Theorems and Problems

Geometry Problem 806
Triangle, Points on sides, Circumcenter, Similarity.

Area of a Right Triangle, Theorems and Problems.

iPad Apps: Apollonius Software. Problem 794: Right Triangle, Altitude, Three Incenters, Circumcircles, Incircle, Congruence.
Interactive Geometry Software.

Geometry Problem 805, Stewart Theorem
Triangle, sides and a cevian.

iPad Apps: Apollonius, Interactive Geometry Software IGS Index.
Theorems and Problems with Apollonius for iPad.

Geometry Problem 804
Circle, Chord, Midpoints.

Geometry Problem 803
Right Triangle, Altitude, Angle Bisector, Perpendicular, Measurement.

Geoboard for iPad Pythagorean Theorem Proof by Leonardo.

Polygon definition

Geoboard for iPad Gallery: Squares inscribed in squares.
Midpoints of the sides, Sequence, Recursive Form, Areas

Geoboard for iPad Gallery: Triangle with two squares (Problem 496).

Geoboard for iPad Gallery: Six squares with a common vertex.

Triangle definition

Geoboard for iPad Index.
This virtual version is an open-ended educational tool, ideal for elementary classrooms and other learning environments that use iPod Touches, iPhones, or iPads

Geoboard for iPad Pythagorean Theorem Proof, Squares (Problem 540).

Geometry Problem 802
Scalene Triangle, Median, Perpendicular, Angle, Measurement.

Geometry Problem 801
Equilateral Triangles, Cevian, Midpoint, Distance, Measurement, Metric Relations.

Geometry Problem 800: de Gua's Theorem
Pythagorean theorem in 3-D, Tetrahedron, Cubic Vertex, Triangular Pyramid, Apex, Height, Right Triangle Area, Base Area, Projected Area.

Geometry Problem 799
Parallelogram, Angle Bisector, Parallel, Triangle, Circumcircle, Circumcenter.

Geometry Problem 798
Parallelogram, Secant Line, Tangent Circles, Circumcircles, Triangle.

Geometry Problem 797
Parallelogram, Angle Bisector, Isosceles and Similar Triangles.

Geometry Problem 796
Triangle, Altitude, Measurement of Angles.

Geometry Problem 795
Intersecting Circles, Common Chord, Midpoint, Tangent, Secant Line, Perpendicular, 90 Degrees.

Geometry Problem 794
Right Triangle, Altitude, Three Incenters, Circumcircles, Incircle, Congruence.

Geometry Problem 793
Right Triangle, Altitude, Three Incircles, Incenters, Circumcircle, Circumradius, Perpendicular, Distance.

Geometry Problem 792
Right Triangle, Altitude, Angle Bisector, Three Incircles, Five Concyclic Points, Circles.

Geometry Problem 791
Regular Hexagon, Midpoints of Side and Diagonal, Equilateral Triangle, Area.

Geometry Problem 790
Right Triangle, Altitude, Angle Bisector, Incircle, Tangency Point, Inradius, Circles, Tangent Line, Congruence.

Geometry Problem 789
Right Triangle, Altitude, Angle Bisector, Incircle, Tangency Point, Inradius, Circles, Tangent Line.

Geometry Problem 788
Intersecting Circles, Secant Line, Midpoint, Cyclic Quadrilateral.

Right triangle, Altitude, Incircle
Right Triangle, Altitude to the Hypotenuse, Incircle, Incenter, Inradius, Angle Bisector, Theorems and Problems, Index.

Geometry Problem 787
Right Triangle, Inradius, 18 Equal Circles, Line Tangent, Legs, Hypotenuse, Ratio, Metric Relations.

Geometry Problem 786
Right Triangle, Altitude, Hypotenuse, Cevian, Perpendicular, Ratio, Metric relations.

Geometry Problem 785
Equilateral Triangle, Parallel, Perpendicular.

Geometry Problem 784
Triangle, Orthocenter, Altitude, Midpoint of a side, Perpendicular.

Geometry Problem 783
Triangle, Orthocenter, Circumcenter, Circumcircle, Diameter, Altitude, Midpoint.

Geometry Problem 782
Triangle, Orthocenter, Circumcenter, Circumcircle, Diameter, Altitude, Parallelogram.

Geometry Problem 781
Triangle, Orthocenter, Circumcenter, Vertex, Altitude, Midpoint, Perpendicular.

Geometry Problem 780
Triangle, Sum of Inradius and Circumradius, Distances from the Orthocenter to the Vertices.

Geometry Problem 779
Triangle, Altitude, Orthocenter, Midpoint, Angle, 90 Degrees.

Geometry Problem 778
Triangle, Distance from the Orthocenter to a Vertex, Circle, Circumradius, Side, Square.

Geometry Problem 777
Triangle, Distance from the Orthocenter to a Vertex, Circle, Circumradius, Cosine.

Geometry Problem 776
Triangle, Isogonal lines, Congruent angles, Perpendicular, Concyclic points, Circle, Center, Midpoint.

Geometry Problem 775
Triangle, Isogonal lines, Congruent angles, Perpendicular, Metric Relations.

Geometry Problem 774
Triangle, Two Altitudes, Circumcircle, Tangent at a Vertex, Parallel.

Geometry Problem 773
Intersecting Circles, Midpoint, Secant line, Bisection.

Geometry Problem 772
Similar triangles with a Common Vertex, Equal Angles, Midpoints, Metric relations.

Geometry Problem 771
Area of a Parallelogram, Star, Pentagon, Triangles.

Geometry Problem 770
Parallelogram, Angle Bisector, Triangle, Circumcenter, Circumcircle, Angle Measurement.

Geometry Problem 769
Triangle, Circumcircle, Circumcenter, Orthocenter, Midpoint of arc, Parallel to chord, Congruence.

Geometry Problem 768
Parallelogram with Equilateral Triangles on Sides.

Geometry Problem 767
Equilateral Triangle, Circle tangent to a side, Tangent line, Measurement, Secant.

Geometry Problem 766
Triangle, Altitudes, Exradii, Three Exradius, Equal Harmonic Mean.

Geometry Problem 765
Triangle, Inradius, Exradii, Three Exradius, Harmonic Mean.

Geometry Problem 764
Triangle, Inradius, Altitudes, Harmonic Mean.

Geometry Problem 763
Parallelogram, Diagonal, Parallel, Congruence.

Geometry Problem 762
Parallelogram, Midpoint, Perpendicular, Congruence, Isosceles triangle.

Geometry Problem 761
Scalene Triangle with an angle of 60 degrees, Euler Line, Equilateral Triangle.

Geometry Problem 760
Isosceles Triangle, Circle, Diameter, Altitude, Chord, Metric relations.

Geometry Problem 759
Equilateral Triangle, Transversal, Trisection of sides, Congruence, Angle.

Geometry Problem 758
Equilateral Triangle, Cevians, Trisection of sides, Congruence, Perpendicular, 90 Degrees.

Geometry Problem 757
Equilateral Triangle, Circumcircle, Chords, a Half of Harmonic Mean.

iPad Apps: Apollonius Software. Four Circles Theorem.
Interactive Geometry Software

Geometry Problem 756: Four Circles Theorem
Using TracenPoche Interactive Dynamic Software.
Step-by-Step construction, Manipulation, and animation.

Geometry Problem 755.
Equilateral Triangle, Circumcircle, Chord, Arc, Midpoints, Perpendicular.

Geometry Problem 754.
Equilateral Triangle, Center, Angle, 60 Degrees, Perimeter.

Geometry Problem 753.
Triangle, Altitudes, Orthocenter, Sum of ratios.

Geometry Problem 752.
Square, Circle, Tangent, Chord, Angle.

Geometry Problem 751.
Parallelogram, Congruence, Intersecting Lines, Angle Bisector.

Geometry Problem 750.
Complete Quadrilateral, Triangle, Diagonal, Parallel, Similarity, Metric Relations.

Geometry Problems 741 - 750.
Triangle, Circle, Quadrilateral, Parallelogram, Trapezoid, Incenter, Circumradius, Parallel, Perpendicular, Orthocenter, Centroid, Similarity, Congruence.

Geometry Problem 749.
Triangle, Rhombus, Parallel, Harmonic Means, Metric Relations.

Geometry Problem 748.
Quadrilateral, 90 Degrees, Diagonal, Perpendicular, Complete Quadrilateral, Metric Relations.

Geometry Problem 747.
Trapezoid, Diagonals, Parallel, Bases, Midpoint, Similarity, Harmonic Mean, Metric Relations.

Geometry Problem 746.
Triangle, Cevian, Parallel, Similarity, Harmonic Mean, Metric Relations.

Geometry Problem 745.
Circle, 90 Degrees, Chord, Congruence, Perpendicular, Metric Relations.

Geometry Problem 744.
Parallelogram, Circle, Diameter, Chord, Congruence, Triangle, Metric Relations.

Harmonic Mean.

Geometry Problem 743.
Trapezoid, Triangle, Perpendicular, Parallel, Angle.

Parallel Chords. Index.
Theorems and Problems.

Geometry Problem 742.
Scalene Triangle, Orthocenter, Centroid, Circumcenter, Circumradius, Midpoint, Distance, Square, Metric Relations.

Geometry Problem 741.
Scalene Triangle, Incenter, Circumcircle, Midpoint, Arc, Congruence.

Top Stadiums in the World by Capacity.

Geometry Problem 740.
Scalene Triangle, Angle, Semi-sum, Cevian, Isosceles Triangle.

Triangle with Double Angle, Theorems and Problems, Index
 

Geometry Problem 739.
Triangle, Double Angle, External Angle Bisector. Congruence.

Common Chord to two circles.
Theorems and Problems.

Geometry Problem 738.
Intersecting Circles, External Common Tangent, Common Chord, Secant, Circumcircle, Cyclic Quadrilateral, Concyclic Points.

Circle Inscribed in a Square, Theorems and Problems. Index.

Geometry Problems 731 - 740.
Triangle, Circle, Quadrilateral, Parallelogram, Circumcircle, Angle Bisector, Semi-sum, Isosceles, Orthocenter, Orthic, Perpendicular, Altitude, Congruence.

Geometry Problem 737.
Cyclic Quadrilateral, Circumscribed Circle, Diameter, Tangent, Perpendicular.

Circle Tangent Line. Index.
Theorems and Problems.
 

Geometry Problem 736.
Triangle, Altitude, Perpendicular,�Angles, Cyclic Quadrilateral.

Top Stadiums in the World by Capacity.

Geometry Problem 735.
Triangle, Altitude, Perpendicular, Semiperimeter of the Orthic Triangle, Congruence.

Perpendicular Chords. Index.
Theorems and Problems.

Geometry Problem 734.
Triangle, Isosceles, Median, Parallel, Angle Bisector, Congruence, Midpoint.

Geometry Problem 733.
Triangle, Orthocenter, Altitude, Reflection in a line, Circumcircle, Concurrency.

Geometry Problem 732.
Triangle, Altitude, Orthic Triangle, Orthocenter, Congruence, Parallelogram.

Geometry Problem 731.
Cyclic quadrilateral, Triangle, Orthocenter, Altitude, Perpendicular, Parallelogram.

Geometry Problem 730.
Triangle, Altitude, Orthocenter, Perpendicular, Concurrent Lines.

Geometry Problem 729.
Triangle, Altitude, Orthocenter, Circumcircle, Perpendicular, Midpoint.

Geometry Problem 728.
Triangle, Altitude, Perpendicular, Circumcircle, Midpoint, Intersecting Circles, Concurrency.

Geometry Problem 727.
Triangle, Isosceles, Congruence, Angles, Measurement.

Geometry Problem 726.
Isosceles Triangle, Perpendicular, Midpoint, 90 Degrees.

Geometry Problem 725.
Kurschak's Dodecagon, Square, Equilateral Triangle, Midpoints, 30, 60 Degrees.

Geometry Problem 724.
Circumscribed Quadrilateral, Circle, Angle, Incenter, Half the Measure.

Geometry Problem 723.
Squares, Circumscribed Circles, Collinear points.

Geometry Problem 722.
Squares, Circumscribed Circles, Collinear points.

Geometry Problem 721.
Triangle, Orthocenter, Circumcircle, Altitude, Collinear points.

Geometry Problem 720.
Excenter, Intersecting Circles, Angle, Measurement.

Geometry Problem 719.
Incenter, Intersecting Circles, Angle, Measurement.

Geometry Problem 718.
Intersecting Circles, Midpoint, Angle, Measurement.

Geometry Problem 717.
Intersecting Circles, Midpoint, Angle, Measurement.

Geometry Problem 716.
Problem 716. Intersecting Circles, Center, Radius, Perpendicular, 90 Degrees.

Area of a Parallelogram.
Theorems and Problems Index.

Geometry Problem 715.
Triangle, Altitudes, Parallel, Circumcircle, Angle, Measurement.

Geometry Problem 714.
Triangle, Parallel, Cevians, Midpoints, Median, Ceva Theorem.

Geometry Problem 713.
Tangent Circles, Diameter, Chord, Tangent, Incenter, Incircle, Triangle.

Geometry Problem 712.
Semicircle, Diameter, Tangent, Perpendicular, Angle Measure.

Geometry Problem 711.
Rectangle, Midpoint, Angle, Concyclic Points, Cyclic Quadrilateral.

Geometry Problem 710.
Parallelogram, Midpoint, Diagonal, Collinear Points, Metric Relations, Triangle, Similarity, Congruence.

Problem Solving Techniques, Interactive Mind Map.

Geometry Problem 709.
Parallelogram, Midpoint, Diagonal, Metric Relations, Triangle.

Geometry Problem 708.
Circle, Tangent, Intersecting, Lune, Area, Diameter.

Geometry Problem 707.
Triangle, Excenters, Excircles, Angle Bisectors, Angle, Measurement.

Geometry Problem 706.
Triangle, Cevian, Three Circumcenters, Circumcircles, Concyclic Points, Cyclic quadrilateral.

Geometry Problem 705.
Intersecting Circles, Diameter, Angles, Measurement.

Geometry Problem 704.
Triangle, Orthocenter, Altitude, Midpoint, Perpendicular.

Geometry Problem 703.
Triangle, Incircle, Tangency point, Diameter, Congruence.

Geometry Problem 702.
Triangle, Circumcircle, Parallel, Concyclic Points.

Geometry Problem 701.
Intersecting Circles, Diameter, Perpendicular, Angles, Congruence.

Concyclic Points.
 

Geometry Problem 700.
Equilateral Triangle, Circle, Circular Segment, Midpoint of a side, Metric Relations.

Geometry Problem 699.
Equilateral Triangle, Circle, Circular Segment, Midpoint, Metric Relations.

Geometry Problem 698.
Quadrilateral, Diagonal, Angle Bisector, Triangle, 120 Degrees.

Geometry Problems 691 - 700.
Triangle, Quadrilateral, Circle, Metric Relations, Square, 30-60-120 Degrees, Area, Congruence.

Geometry Problem 697.
Square, Circle, Sector, Segment, Tangent, Inscribed, Congruence, Mind Map, Polya.

Geometry Problem 696.
Triangle, Angles, Auxiliary Construction, Congruence, Mind Map, Polya.

Geometry Problem 695.
Triangle, Angles, Auxiliary Construction, Congruence, Mind Map, Polya.

Geometry Problem 694.
Triangle, Angles, 30 Degrees, Auxiliary Construction, Mind Map, Polya.

Geometry Problem 693.
Square, Inscribed and Circumscribed Circle, Areas, Mind Map, Polya.

Geometry Problem 692.
Quatrefoil, Four Equal Circles and a Circle Inscribed in a Square, Areas, Mind Map, Polya.

Geometry Problem 691.
Isosceles Triangle, 80-80-20 Degrees, Angles, Congruence, Mind Map, Polya.

Problem 690: Distance between the Incenter and the Centroid of a Triangle.
Formula in terms of the sides a,b,c.

Geometry Problems 681 - 690.
Triangle, Circle, 60 Degrees, Incenter, Circumcenter, Orthocenter, Parallelogram, Metric Relations, Congruence, Similarity.

Geometry Problem 689.
Triangle, Three Excircles, Tangency points, Tangent lines, Concurrent Lines, Mind Map.

Geometry Problem 688.
Triangle, Angles, 10, 20, 30, 40, 60 Degrees, Measure, Mind Map, Polya.

Geometry Problem 687.
Triangle, Three Excircles, Tangency points, Concurrent Lines.

Geometry Problem 686.
Triangle, Three Excircles, Tangency points, Tangent lines, Semi-perimeter, Congruence.

Geometry Problem 685
Isosceles Triangle, 100-40-40 Degrees, Angles, Congruence.

Geometry Problem 684: Outer Nagel Point.
Triangle, Excircles, Incircle Tangency points, Concurrent lines, Semi-perimeter, Ceva theorem.

Geometry Problem 683: Nagel Point.
Triangle, Excircles, Tangency points, Concurrent lines, Semi-perimeter, Ceva theorem.

Geometry Problem 682: Gergonne External Point.
Triangle, Excircle, Tangency points, Concurrent lines, Semiperimeter, Ceva theorem.

Geometry Problem 681: Gergonne Point.
Triangle, Incircle, Tangency points, Concurrent lines, Semiperimeter, Ceva theorem.

Geometry Problem 680.
Concentric Circles, Radii, Chords, Perpendicular, Metric Relations.

100 Geometry Problems Collection

Geometry Problem 679.
Triangle, Circle, Median, Proportion.

Geometry Problem 678.
Triangle, Simson Line, Circumcircle, Tangent, Parallel, Perpendicular, Collinear Points.

Geometry Problem 677.
Parallelogram, Midpoint, Diagonal, Metric Relations.

Geometry Problem 676.
Circles, Diameter, Tangent, Chord, Metric Relations.

Geometry Problem 675.
Intersecting Circles, Secant, 45 and 90 Degrees, Collinear Points.

Geometry Problem 674.
Triangle, Altitude, Angles.

Geometry Problem 673.
Internally tangent circles, Chord, Tangent, Metric Relations.

Geometry Problem 672.
Internally tangent circles, Chord, Tangent, Geometric Mean.

Geometry Problem 671.
Triangle, Cevian, Angles, Congruence.

Geometry Problem 670.
Triangle, 60 Degrees, Orthocenter, Incenter, Circumcenter, Congruence.

Geometry Problem 669.
Triangle, Circumcircle, Incenter, Midpoint, Collinear points, Mind Map.

Geometry Problem 668.
Right triangle, Incircles, Parallel, Common Tangent, Mind Map.

Geometry Problem 667.
Intersecting Circles, Secant, Tangent, Metric Relations, Mind Map.

Geometry Problem 666.
Intersecting Circles, Secant, Tangent, Concyclic points, Mind Map.

Geometry Problem 665.
Intersecting Circles, Secant, Tangent, Angles, Mind Map.

Geometry Problem 664.
Triangle, 60 Degrees, Orthocenter, Incenter, Circumcenter, Angles, Triangle centers.

Geometry Problem 663.
Scalene Triangle, 60 Degrees, Altitude, Angle Bisector, Perpendicular Bisector, Concurrent lines.

Video solution: Problems 1-6 (Spanish version)
By Eder Contreras and Cristian Baeza, Chile.

Geometry Problem 662.
Triangle, Incenter, Circumcenter, Orthocenter, Circle, Angle, Measurement.

Geometry Problem 661.
Intersecting Circles, Centers, Secant, Parallelogram.

Geometry Problem 660.
Triangle, Circle, Diameter, Perpendicular Lines.

Geometry Problem 659.
Parallelogram, Parallel Lines, Collinear Points.

Geometry Problem 658.
Triangle, Altitudes, Diameter, Circle, Angles.

Geometry Definitions.

Geometry Problem 657.
Triangle, Incircle, Tangency Points, Parallel Lines, Congruence.

Geometry Definitions.

Geometry Problem 656.
Triangle, Cevian, Concurrent Lines.

Dynamic Geometry Software: GeoGebra 3.2 Help Document
GeoGebra is a dynamic geometry software. Constructions can be made with points, vectors, segments, lines, polygons, conic sections, and functions.
Interactive Mind Map

Geometry Problem 655.
Archimedes Book of Lemmas: Proposition 15
Circle, Inscribed Regular Pentagon, Radius.

Semicircle. Index.
Theorems and Problems.

Geometry Problem 654.
Archimedes Book of Lemmas: Proposition 14
Salinon, Semicircles, Diameter, Circle, Area.

Geometry Problem 653.
Archimedes Book of Lemmas: Proposition 13
Circle, Chord, Perpendicular, Congruence.

Geometry Problem 652.
Archimedes Book of Lemmas: Proposition 12
Perpendicular chords, Arcs, Radius.

Geometry Problem 651.
Archimedes Book of Lemmas: Proposition 11
Perpendicular chords, Arcs, Radius.

Geometry Problem 650.
Tangent Circles, Diameter, Radius, Chord, Perpendicular.

Geometry Problem 649.
Archimedes Book of Lemmas: Proposition 10
Tangent, Chord, Parallel, Midpoint.

Geometry Problem 648.
Archimedes Book of Lemmas: Proposition 9
Perpendicular chords, Arcs.

Geometry Problem 647.
Archimedes Book of Lemmas: Proposition 8
Angle trisection. Neusis construction.

Geometry Problem 646.
Archimedes Book of Lemmas: Proposition 7
Square,Inscribed and Circumscribed Circles, Area.

Geometry Problem 645.
Archimedes Book of Lemmas: Proposition 6
Semicircle, Circle, Perpendicular, Arbelos, Inscribed Circle.

Geometry Problem 644.
Archimedes Book of Lemmas: Proposition 5
Semicircle, Circle, Perpendicular, Arbelos, Archimedean Twins.

Geometry Problem 643.
Archimedes Book of Lemmas: Proposition 4
Semicircle, Circle, Perpendicular, Arbelos, Area.

Arbelos Definition by Archimedes
Three Semicircles, Tangent, Diameters.

Geometry Problem 642.
Archimedes Book of Lemmas: Proposition 3
Semicircle, Perpendicular, Arc, Midpoint, Congruence.

Geometry Problem 641.
Archimedes Book of Lemmas: Proposition 2
Semicircle, Tangent, Perpendicular, Midpoint.

Geometry Problem 640.
Archimedes Book of Lemmas: Proposition 1
Tangent circles and parallel diameters 

Geometry Problem 639
Semicircle, Diameter, Perpendicular, Inscribed Circle, Tangent, Arbelos, Congruence.

Perpendicular Bisector.

Geometry Problem 638
Arbelos and Inscribed Circle: Concyclic Points.

Geometry Problem 637
Semicircle, Diameter, Perpendicular, Inscribed Circle, Chord, Tangent, Arbelos.

Geometry Problem 636
Semicircle, Diameter, Perpendicular, Inscribed Circle, Common Tangent.