Geometry Theorems and Problems - Recent Additions (Page 5 of 15)

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.

Geometry Problem 635
Semicircle, Diameter, Perpendicular, Inscribed Circle, Radius.

Geometry Problem 634
Right Triangle, Altitude, Incenters, Areas.

Geometry Problem 633
Triangle, Parallel Lines, Intersecting Lines.

Geometry Problem 632.
Triangle, Interior and Exterior Angle Bisectors, Midpoints, Collinear Points.

Geometry Problem 631.
Triangle, Exterior Angle Bisectors, Collinear Points.

Clawson Point.
Orthic and Extangents Triangles, Concurrent lines.

Clawson Point Puzzle, Geometry for Kids.
22 Piece Polygons

Triangle Incenter by Folding, Video .
Dynamic Geometry Software: Tabula by Numeracy Works.
Step-by-Step construction, Manipulation, and animation.

Triangle Circumcenter by Folding, Video.
Dynamic Geometry Software: Tabula by Numeracy Works.
Step-by-Step construction, Manipulation, and animation.
Perpendicular Bisectors.

Geometry Problem 629
Triangle, Perpendicular to Sides, Intersecting Lines, Altitude.

Geometry Problem 628
Cyclic Quadrilateral, Congruence, Parallel Lines.

Sangaku Japanese Geometry
Seventeenth and nineteenth centuries.

Triangle Orthocenter by Folding, Video.
Dynamic Geometry Software: Tabula by Numeracy Works.
Step-by-Step construction, Manipulation, and animation.

Triangle Centroid by Folding, Video.
Dynamic Geometry Software: Tabula by Numeracy Works.
Step-by-Step construction, Manipulation, and animation.

Geometry Problem 627
Cyclic Quadrilateral, Congruence, Concyclic Points.

Geometry Problem 626
Triangle, Distance from the Incenter to an Excenter.

Geometry Problem 625
Triangle, Parallel Lines, Congruence, Angle Bisector.

Geometry Problem 624
Triangle, Incenter, Excenter, Incircle, Excircle, Similarity.

Geometry Problem 623
Triangle, Incenter, Excenter, Incircle, Excircle, Concyclic Points.

Geometry Problem 622
Square with Perpendiculars, Transversal, Congruence.

Geometry Problem 621
Three Rectangles, Diagonals, Centers, Angles.

Geometry Problem 620
Three Rectangles, Diagonals, Centers, Angles.

Geometry Problem 619
Triangle Area, 30 Degrees, Incircle, Incenter, Tangent.

Geometry Problem 618
Triangle Area, 60 Degrees, Incircle, Incenter, Tangent.

Geometry Problem 617
Right Triangle Area, Incircle, Incenter, Tangent, 90 Degrees.

Geometry Problem 616
Parallelogram, Diagonals, Intersecting Lines, Parallel Lines.

Geometry Problem 615
Right Triangle with a Square, Diagonals, Center, Area of Quadrilateral.

Geometry Problem 614
Parallelogram, Diagonals, Intersecting Lines, Parallel Lines.

Geometry Problem 613
Altitude of a Triangle, Perpendicular, Collinear Points.

Geometry Problem 612
Altitude of a Triangle, Perpendicular, Congruence.

Geometry Problem 611
Altitude of a Triangle, Perpendicular, Collinear Points, Parallel.

Geometry Problem 610
Intersecting Circles, Radius, Parallel,
Common Tangent, Angle, 90 Degrees.

Geometry Problem 609
Triangle, Perpendiculars, 90 Degrees, Collinearity.

Geometry Problem 608
Square with Right Triangles, Metric Relations, Congruence, Measurement.

Geometry Problem 607
Intersecting Circles, Triangles, Metric Relations, Measurement.

Geometry Problem 606
Isosceles Triangles, Perpendicular and Parallel Lines.

Geometry Problem 605
Circle, Square, Chord, Perpendicular, Circular Segment, Metric Relations.

Geometry Problem 604
Parallelograms, Triangle, Trapezoid, Area.

Geometry Problem 603
Parallelogram, Diagonals, Congruence, Concurrency.

Geometry Problem 602
Triangle, Angles, 30 and 45 Degrees, Cevian, Congruence.

Geometry Problem 601
Cyclic Quadrilateral, Incenter, Excenter, Rectangle.

Brianchon's Theorem in a Circumscribed Hexagon.

Brianchon Corollary, Circumscribed Hexagon, Concurrency lines.

Carnot's Theorem in an Acute Triangle.

Carnot's Theorem in an Obtuse Triangle.

Geometry Problem 600
Circle, Area, Tangent, Semicircle, Tangency Point.

Geometry Problem 599
Regular Hexagon, Square, Midpoint, Angle, Degrees.

Geometry Problem 598
Trapezoid, Perpendicular, Equal Angles, Metric Relation.

Geometry Problem 597
Quadrilateral, Right Triangle, Isosceles, Angle, Congruence.

Geometry Problem 596
Quadrilateral, Right Triangle, Isosceles, Midpoint.

Geometry Problem 595
Triangle, Equal Angles, Isogonal Conjugate, Similarity.

Open Geometry Problems - Index

Geometry Problem 594.
Triangle, Incenter, Incircle, Inradius, Tangency Point, Midpoint, Altitude, Angle, Half the Difference.

Geometry Problem 593.
Triangle, Circumcircle, Collinear Points.

Geometry Problem 592.
Triangle, Incenter, Incircle, Tangency Point, Midpoints, Concurrent Lines, Congruence.

Geometry Problem 591.
Triangle, Incenter, Incircle, Inradius, Tangency Point, Midpoint, Altitude.

Geometry Problem 590.
Triangle, Incenter, Incircle, Tangency Point, Midpoint, Areas.

Geometry Problem 589.
Triangle, Incenter, Incircle, Tangency Points, Midpoint, Perpendicular, Distance.

Geometry Problem 588.
Triangle, Incenter, Incircle, Tangency Points, Midpoints, Distance, Sum.

Geometry Problem 587.
Triangle, Incenter, Incircle, Tangency Point, Midpoint, Distance, Half the Difference.

Geometry Problem 586.
Cyclic Quadrilateral, Diagonals, Any Point, Circumcenters, Circumcircles, Concurrency.

Problem 585.
Cyclic Quadrilateral, Diagonals, Circumcenters, Circumcircles, Concurrency.

Problem 584.
Cyclic Quadrilateral, Diagonals, Circumcenters, Circumcircles, Parallelograms.

Problem 583.
Quadrilateral, Diagonals, Circumcenters, Parallelogram, Octagon, Areas.

Problem 582.
Quadrilateral, Diagonals, Incenters, Metric Relations.

Problem 581.
Volume of two Triangular Pyramids, Equal Trihedral Angle, Product of three Edges.

Geometry Problems 581 - 590.
Quadrilateral, Diagonals, Concurrency, Incenter, Metric Relations, Circumcenters, Parallelogram, Octagon, Areas, Tangency Point, Midpoint, Cyclic Quadrilateral, Volume of two Triangular Pyramids, Equal Trihedral Angle, Product of three Edges.

Problem 580.
Triangles, Equal Angle, Transversal, Product of Sides, Areas.

Problem 579.
Quadrilateral, Diagonals, Triangles, Areas.

Area of a Triangle, Theorems and Problems, Index.

Problem 578.
Circle, Perpendicular Chords, Midpoints, Curvilinear Triangle, Area, 90 Degrees.

Metric Relations in a Right Triangle, Theorems and Problems.

Problem 577.
Isosceles triangle, Midpoint, Perpendicular, Concyclic points, Circle.

Diameters and Chords, Theorems and Problems. Index.

Problem 576.
Centroid, Triangle, Quadrilateral, Parallel, Measurement.

Problem 575.
Cyclic quadrilateral, Angle bisector, Measurement.

Intersection of a Line with a Circle
 

Problem 574.
Circle, Chord, Secant, Angle Bisector, Perpendicular.

Problem 573.
Cyclic quadrilateral, Angle bisector, Perpendicular.

Problem 572.
Right triangle, Median, Circle, Diameter, Excircle, Tangent circles.

Problem 571.
Circle, Diameter, Chord, Perpendicular, Measurement.

Problem 570.
Square, Center, Right Triangles, Congruence, Collinearity.

Problem 569.
Quadrilateral, Excircles, Tangency Points, Congruence.

Problem 568.
Triangle, Excircles, Tangency Point, Congruence.

Geometry Problems 561 - 570.
Right Triangle, Altitude, Angle Bisector, Congruence, Median, Area, Trisector, 60 Degrees, Equilateral, Parallel, Transversal, Circumcircle, Concyclic, Similarity.

Geometry Problems 551 - 560.
Right Triangle, Altitude, Angle Bisector, Congruence, Median, Area, Trisector, 60 Degrees, Equilateral, Parallel, Transversal, Circumcircle, Concyclic, Similarity.

Problem 567.
Right triangle, Incircle, Excircle, Collinear tangency points.

Problem 566.
Quadrilateral, Diagonals, Parallel.

Problem 565.
Triangle, Isogonal lines, Angles, Congruence, Concyclic Points.

Problem 564.
Complete Quadrilateral, Incenter, Excenter, Concyclic Points, Incircle, Excircle.

Problem 563.
Regular Pentagon, Center, Rectangle, Diagonals, Angle.

Problem 562.
Triangle, Cevian, Incenter, Perpendicular, Concyclic Points, Cyclic Quadrilateral.

Problem 561.
Triangle, Cevian, Incenter, Incircle, Perpendicular, Tangent.

Problem 560.
Triangle, Cevian, Incenter, Incircle, Perpendicular, Tangent.

Problem 559.
Triangle, Cevian, Incenters, Angle, 90 Degrees.

Problem 558.
Quadrilateral, Trisection, Sides, Wittenbauer Parallelogram, Area, Auxiliary Lines.

Problem 557.
Quadrilateral, Midpoints, Sides, Varignon Parallelogram, Area, Auxiliary Lines.

Problem 556.
Quadrilateral, Diagonal, Angles, Auxiliary Lines.

Problem 555.
Parallel lines, Angle Sums.

Problem 554.
Concave Quadrilateral, Angles, Sum.

Problem 553.
Quadrilateral, Angles, Sum.

Problem 552.
Parallel lines, Transversal, Angle Sums.

Problem 551.
Parallel lines, Transversal, Angle Sums.

Problem 550.
Parallel lines, Transversal, Angle Sums.

Problem 549.
Parallel lines, Transversal, Angle Sums.

Problem 548.
Triangle, Transversal, Four Circumcircles, Circumcenters, Concyclic Points, Similarity.

Problem 547.
Triangle, Transversal, Four Circumcircles, Concurrency.

Circumcircle Index.

Problem 546.
Triangle, Angle Trisectors, 60 Degrees, Equilateral triangle.

Problem 545.
Acute Triangle, Squares, Altitudes, Area, Measure.

Problem 544.
Right Triangle, Altitude, Median, Equal angles, Measure.

Geometry Problems 341 - 350.
Triangle, Quadrilateral, Pentagon, Hexagon, Inscribed circle, Tangent, Semiperimeter, Equal circles, Concurrent lines, Altitude, Concyclic Points, Cevian, Incircle.

Problem 543.
Right Triangle, Altitude, Angle Bisector, Median.