Geometry Theorems and Problems - Recent Additions (Page 8 of 15)

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.

Problem 542.
Right Triangle, Altitude, Angle Bisector, Perpendicular, 90 Degrees.

Problem 541.
Right Triangle, Altitude, Angle Bisector, Congruence.

Geometry Problems 331 - 340.
Square, Circle, Similarity, Cyclic quadrilateral, Trapezoid, Triangle, Isosceles, Circumcircle, Incircle, Diagonal, Tangent, Perpendicular, Parallel, Concyclic points.

Geometry Problems 321 - 330.
Triangle, Square, Circle, Area, Cyclic quadrilateral, Tangent, Incenter, Circumcenter, Excircle, Midpoint, Altitude, Collinearity, Concurrence, Isosceles, Equilateral, Parallel, Perpendicular, Diameter, Concyclic.

Geometry Problems 311 - 320.
Circle, Semicircle, Chord, Diameter, Tangent, Cyclic quadrilateral, Geometric mean, Square, Right triangle, Altitude, Collinearity, Circumcircle, Incenter, Excenter.

Geometry Problems 301 - 310.
Circle, Tangent, Secant, Square, Triangle, Angle Bisector, 45, 60, 90, 120 Degrees, Side, Nonagon, Midpoint, Arc, Diagonal, Semicircle.

Geometry Problems 231 - 240.
Triangle, Quadrilateral, Square, Parallelogram, Trapezoid, Altitude, Distances, Midpoint, Perpendicular, Transversal.

Problem 540.
Right Triangle, Square, Parallel, Perpendicular, Dissection, Area, Pythagoras.

Geometry Problems 291 - 300.
Triangle, Circle, Square, Congruence, Similarity, Circumradius, Perpendicular, Parallel, Secant, Tangent, Chord, Intersection, Midpoint, Radius, Angle.

Problem 539.
Right Triangle, Square, Parallel, Perpendicular, Dissection, Area, Pythagoras.

Geometry Problems 281 - 290.
Triangle, Square, Circle, Octagon, Congruence, Isosceles, Equilateral, 90 Degrees, Circular Sector, Semicircle, Tangent, Radius, Diameter, Harmonic Mean.

Problem 538.
Triangle, Perpendicular Bisector, Circumcircle, Midpoint.

Problem 537.
Rectangle, Midpoints, Diagonal, Angle Bisector.

Problem 536.
Intersecting Circles, Chord, Perpendicular.

Problem 535.
Sawayama - Thebault's theorem: Triangle, Incircle, Circle, Center, Tangent, Collinear.

Problem 534.
Right Triangle, Squares, Perpendicular, Dissection, Areas.

Geometry Problems 271 - 280.
Circle, Quadrilateral, Square, Tangent, Cube, Triangle, Isosceles, Area, 90-80-80-20 Degrees, Circumcircle, Sagitta, Inradius, Chord, Perpendicular.

Geometry Problems 261 - 270.
Regular Polygon, Pentagon, Hexagon, Circle, Tangent, Similarity, Triangle, Hypotenuse, Catheti, Geometric Mean, Altitude, Projection, Fractional Exponent.

Problem 533.
Euclid's Elements, Book XIII, Proposition 10. One page visual illustration.

Geometry Problems 251 - 260.
Parallelogram, Rectangle, Triangle, Square, Circle, Area, Side, Equilateral, Isosceles, Centroid, Distance, Vertex, Circumcircle, Incircle, Tangent, Diagonal.

Brahmagupta Theorem and Problems - Index
Brahmagupta (598–668) was an Indian mathematician and astronomer who discovered a neat formula for the area of a cyclic quadrilateral.

Solid Geometry: Morphing Platonic Solids. Sacred geometry, Video and News.

Problem 532.
Triangle, Circumcircle, Equal Angles, Perpendicular, Area.

Ptolemy's Theorems and Problems - Index.

Semiperimeter, Perimeter Index.
Theorems and Problems.

Problem 531.
Triangle, Angle Bisector, Midpoint, Parallel, Perimeter, Semiperimeter.

Geometry Problems 241 - 250.
Triangle, Quadrilateral, Congruence, Area, Parallelogram, Square, Diagonal, Center, Napoleon, Median, Midpoint.

Problem 530.
Cyclic Quadrilateral, Diagonal, Diameter, Perpendicular, Congruence.

Problem 529.
Right Trapezoid, Circle, Diameter.

Problem 528.
Triangle, Medians, Perpendicular, Measurement.

Problem 527.
Circle, Tangent, Secant, Chord, Midpoint, Measurement.

Problem 526.
Equilateral Triangle, Circumcircle, Chord, Measurement.

Geometry Problems 221 - 230.
Isosceles, Equilateral triangle, Viviani's theorem, Altitude, Distances, Regular Polygon, Apothem, Centroid, Midpoint, Perpendicular, Transversal..

Problem 525.
Circles, Diameter, Tangent, Radius, Congruence, Measurement.

Problem 524.
Circle, Equilateral Triangles, Midpoint, Side, Measurement.

Problem 523.
Tangent Circles, Diameter Perpendicular, Collinearity.

Problem 522.
Right Triangle, Circle, Diameter, Tangent.

Problem 521.
Triangle with three Squares, Altitude, Rectangle, Area.

Geometry Problems 211 - 220.
Equilateral triangle, Quadrilateral, Area, Cyclic Quadrilateral, 60 Degree, Angle Bisector, 120, incircle, Inradius, Semicircle, Tangent, Concurrency, Right triangle, Altitude, Projection, Rhombus, Perpendicular, Arithmetic Mean, Distance.

Problem 520.
Triangle with six Squares, Ratio, Area.

Problem 519.
Triangle, Squares, Altitude, Perpendicular, Rectangle, Area.

Geometry Problems 191 - 200.
Triangle, Circle, Square, Area, Circle, Diameter, Altitude, Orthocenter, Semiperimeter, Inradius, Exradius, Quadrilateral, Angle, Tangent, Right triangle.

Problem 518.
Parallelogram, Five Squares, Centers, 45 Degrees, Measure.

Problem 517.
Right Triangle, Six Squares, Areas.

Problem 516.
Triangle, Cevian, Congruence, Angles.

Problem 515.
Triangle, Double Angle, Altitude, Measure.

Geometry Problems 181 - 190.
Right Triangle, Trapezoid, Square, Intersecting Circles, Circular Sector, 90 Degrees, Angles, Trisection, Hypotenuse, Distance, Incenter, Altitude, Diagonal, 45 Degrees, Tangent, Chord, Perpendicular.

Problem 514.
Triangle, Five Squares, Line, Area.

Problem 513.
Triangle, Double Angle, Exterior Angle Bisector, Measure.

Geometry Problems 171 - 180.
Area, Triangle, Quadrilateral, Circle, Parallelogram, Trapezoid, Square, Rhombus, Diagonal, Angle, Tangent, Trisection.

Geometry Problems 161 - 170.
Area, Triangle, Parallelogram, Trapezoid, Pentagon, Diagonal, Midpoint, Octagon.

Problem 512.
Triangle with three squares and concurrency.

Problem 511.
Triangle, Double Angle, Angle Bisector, Measure.

Problem 510.
Triangle, Three Squares, Midpoints, Concurrency.

Problem 509.
Triangle, 120 Degrees, Angles, Congruence, Mind Map.

Geometry Problems 151 - 160.
Triangle, Quadrilateral, Area, Trisection, Circle, Proportion, Diagonal, Chord,Inradius, Circumradius, Exradius, Euler, distance, Incenter, Circumcenter, Excenter, Incircle, Circumcircle.

Problem 508.
Triangle with three Squares, Four triangle of equal Area.

Problem 507.
Triangle, Interior Point, 120 Degrees, Congruence, Angle.

Problem 506.
Triangle with Three Squares, Center, Midpoint, Perpendicular.

Problem 505.
Right Triangle, Cevian, Sum of Segments, Angles.

Problem 504.
Equilateral Triangle, Angles, 45, 60 Degrees.

Ten Geometry Problems, Visual Index

Problem 503.
Triangle with Three Squares, Perpendicular, Congruence, Concurrency.

Geometry Problems 141 - 150.
Triangle, Quadrilateral, Parallelogram, Incircle, Incenter, Tangent, Parallel, Perimeter, Area, Inradius, Circumradius, Midpoint, Varignon, Trisection.

Problem 502.
Triangle, Two Squares, Midpoint, Perpendicular, Half the measure.

Problem 501.
Triangle, Two Squares, Center, Midpoint, another Square.

Problem 500.
Circle, Diameter, Chord, Perpendicular, Measure.

Problem 499.
Triangle, Two Squares, Perpendicular.

Problem 498.
Triangle, Angle Bisector, Double Angle, Measure.

Problem 497.
Triangle, Two Squares, Centers, Midpoint, 90 Degrees.

Problem 496.
Triangle, Two Squares, 90 Degrees, Concurrency, Angle Bisectors.

Problem 495.
Triangle, 120 Degrees, Angle Bisectors.

Geometry Problems 121 - 130.
Triangle, Area, Similarity, Trisection, Hexagon, Star, Incenter, Centroid, Parallel, Proportions, Angle Bisector, Ratio

Problem 494.
Circular Sector, 90 Degrees, Semicircle, Chord, Parallel.

Geometry Problems 111 - 120.
Orthogonal Circles, Triangle, Square, Area, Incircle, Excircle, Tangent, Incenter

The Simson Line, Theorems and Problems - Index.

Geometry Problems 101 - 110.
Angle, Equilateral Triangle, Pythagorean Theorem, Median, Heron, Cevian, Contact Triangle.

Problem 493.
Right Triangle, Circumcircle, Perpendicular, Chord.

Problem 492.
Cyclic Quadrilateral, Circle, Perpendicular, Side, Diagonal, Parallel.

Geometry Problems 91 - 100.
Similarity, Triangles, Altitude, Parallel, Circumcircle, Parallelogram, Incenter, Area, Centroid, Quadrilateral, Archimedes, Pythagoras.

Problem 491.
Square, Right Triangle, Incircle, Inscribed Circle, Radius.

Geometry Problems 81 - 90.
Triangle, Quadrilateral, Circle, Incircle, Circumcircle, Excircle, Inradius, Circumradius, Exradius, Contact Triangle, Area, Midpoint.

Problem 490.
Tangent Circles, Arc, Radius, Circular Sector, Area.

Problem 489.
Parallelogram, Triangle, Quadrilateral, Area.

Problem 488.
Triangle, Cevian, Concurrency, Circle, Circumcircle.

Geometry Problems 71 - 80.
Cyclic Quadrilateral, Intersecting Circles, Area, Inradius, Incircle.

Problem 487.
Intersecting Circles, Area, Diameter, Parallel, 90 Degrees.

Problem 486.
Tangent circles, Chord, Arc, Midpoint, Collinearity, Congruence.

Problem 485.
Square, Side, Circles, Tangent, Radius, Measurement.

Problem 484.
Square, Angle, 90 degrees, Triangle, Measurement, Proportion.

Geometry Problems - Visual Index.

Problem 483.
Square, Angle, 90 degrees, Measurement.

Problem 482.
Triangle, Circumcircle, Incenter, Excenter, Midpoint, Cyclic Points.

Problem 481.
Triangle, Altitude, Cevian, Perpendicular, Angle.

Geometry Problems 61 - 70.
Triangle, Quadrilateral, Circle, Cyclic, Similarity.

Problem 480.
Triangle, Circle, Center, Altitude, Angle, Circumcenter.

Problem 479.
Triangle, Cevians, Concurrency, Transversal, Proportion.

Problem 478.
Triangle, Sides, Circumradius, Circumcenter, Circumcircle.

Problem 477.
Parallelogram, Triangle, Quadrilateral, Area.

Geometry Problems 51 - 60.
Triangle, Quadrilateral, Circle, Cyclic Quadrilateral.

Problem 476.
Triangle, Circumcenter, Circumcircle, Angles.

Problem 475.
Tangent Circles, Secant, Tangent, Parallel.

Geometry Problems 41 - 50.
Triangle, Sangaku, Quadrilateral, Circle, 30-60 Degrees.

Problem 474.
Parallelogram, Diagonal, Circle, Vertex.

Problem 473.
Triangle, Parallel, Side, Parallelogram, Area, Similarity.

Problem 472.
Triangle, Parallel, Side, Parallelogram, Area, Similarity.

Geometry Problems 21 - 30.
Right triangle, Altitude, Incircle and inradius, Congruence, Circle.

Problem 471.
Triangle, Parallel, Side, Concurrency, Area, Similarity.

Geometry Problems 11 - 20.
Angle, Angle bisector, Triangle, Altitude, Median, Congruence, Cevian, Circle, Excircle, Excenter, Inradius, Exradius

Problem 470.
Triangle, Parallel, Side, Parallelogram, Area, Similarity.

Geometry Problems 1 - 10.
Angle, Triangle, Quadrilateral, Congruence, 20, 30, 45, 60, 80, 120 degrees, Median, Auxiliary lines.

Proposed Problem 469.
Isosceles triangle, Midpoint, Transversal, Congruence.

Proposed Problem 468.
Circle, Chord, Midpoint, Congruence, Angle.

Proposed Problem 467.
Concentric Circles, Chord, Tangent, Congruence, Measurement.

Proposed Problem 466.
Concentric Circles, Secant, Congruence, Measurement.

Proposed Problem 465.
Square, Arc, Angle, 90 Degrees, Measurement.

Napoleon's theorems and problems, Index.

Proposed Problem 464.
Square, Arcs, Center, Angle, 90 Degrees, 120 Degrees.

Concentric Circles. Index.
Theorems and Problems. 

Concentric Circles Definition.

Proposed Problem 463.
Three Concentric Circles, Secant, Tangent, Triangle, Area.

Proposed Problem 462.
Square, Arcs, 90 Degrees, Circle, Tangent, Radius, Measurement.

Proposed Problem 461.
Three Circles, Tangent, Right Angle, Center, Distance, Measurement.

Proposed Problem 460.
Circle, Tangent, Perpendicular, Radius, Distance, Measurement.

Proposed Problem 459.
Right triangle, Squares, Distance, Measurement.

Proposed Problem 458.
Square, Semicircle, Circular Sector, Internal Common Tangent, Measurement.

Proposed Problem 457.
Triangle, First Brocard Point, Congruent angles, Circle, Circumradius.

Proposed Problem 456.
Three tangent circles, Center, Chord, Secant, Collinear.

Proposed Problem 455.
Rhombus, Inscribed Circle, Angle, Chord, 45 Degrees.

Proposed Problem 454.
Triangle, Incircle, Inradius, Tangent, Circle, Radius.

Proposed Problem 453.
Intersecting Circles, Tangent, Circular Segment, Congruence, Area.

Triangle Centers, Visual Index.

Fermat Point.
 

Vecten Outer Point.
 

Proposed Problem 452.
Triangle, Circle, Tangent, Proportional Segments.

Proposed Problem 451.
Triangle, Median, Congruence, Proportional Segments.

Proposed Problem 450.
Triangle, Median, Cevian, Congruence, Proportional Segments.

Proposed Problem 449.
Congruent Tangent Circles, Diameter, Sagitta, Arc, Perpendicular, Chord.

Proposed Problem 448.
Tangent Circles, Diameter, Perpendicular, Chord.

Proposed Problem 447.
Complete Quadrilateral, Inradii, Exradii, Sides.

Complete Quadrilateral Index.
 

Proposed Problem 446.
Quadrilateral Area, Dividing the sides into 5 equal parts.

Proposed Problem 445.
Three Tangent Circles, Tangency Points, Circumradius.

Proposed Problem 444.
Internally Tangent circles, Secant line, Chords, Angles, Congruence.

Proposed Problem 443.
Overlapping, Intersecting Circles, Common Chord, Secant line, Tangent line, Angles.

Proposed Problem 442.
Triangle, Median, Cevian, Transversal, Congruent Angles.

Proposed Problem 441.
Quadrilateral, Triangle, Area, Proportion, Measurement, Similarity.

Proposed Problem 440.
Triangle, Incircle, Incenter, Angle Bisector, Tangency Points, Circle, Angles.

Marion Walter's Theorem and Related Topics: Index

Proposed Problem 439.
Isosceles triangle, Cevian, Incenter, Angles, Circle.

Proposed Problem 438.
Tangent Circles, Diameter, Chord, Perpendicular, Congruence, Measurement, Parallel lines.

Proposed Problem 437.
Tangent Circles, Diameter, Chord, Perpendicular, Congruence, Measurement.

Proposed Problem 436.
Tangent Circles, Diameter, Chord, Perpendicular, Congruence, Measurement.

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

Distances between Triangle Centers Index.

Proposed Problem 435.
Triangle, Incircle, Inradius, Congruent circles, tangent, Measurement.

Proposed Problem 434.
Quadrilateral, Transversal, Ratio, Measurement, Similarity.

Proposed Problem 433.
Quadrilateral, Triangle, Area, Proportion, Measurement, Similarity.

Proposed Problem 432.
Trapezoid, Parallel, Measurement, Similarity, Transversal.

Proposed Problem 431.
Quadrilateral, Midpoints of Diagonals, Transversal.

Transversal Lines.

Proposed Problem 430.
Circumscribed and Inscribed Regular Pentagon, Perpendicular, Areas.

Obtuse Angle. Theorems and Problems.

Isosceles Triangle 80-20-80. Index

Proposed Problem 429.
Circumscribed and Inscribed Regular Pentagon, Perpendicular, Measurement.

Proposed Problem 428.
Quadrant of a circle, Square, Angle bisector, Measurement.

Euclid's Elements Book I, Proposition 8: (Side-Side-Side SSS Congruence)

Euclid's Elements Book I, Proposition 7
Given two straight lines constructed on a straight line (from its extremities) and meeting in a point,...

Proposed Problem 427.
Triangle, Two Altitudes, Square of a Side.

Proposed Problem 426.
Triangle, Circumradius, Circumcenter, concurrent Cevians.

Euclid's Elements Book I, Proposition 5: (Pons Asinorum) Isosceles triangles

Area of a Square Index.

Euclid's Elements Book I, Proposition 6: Converse of I.5

Proposed Problem 425.
Quadrilateral, Triangle, Angles, 10, 20, 50 degrees, Congruence.