Inca Trail to Machu Picchu, the Lost City of the Incas

Welcome to Geometry Theorems and Problems! Level: High School, SAT Prep, College geometry

Mind Map of How to Solve Problems
George Pólya's 1945 book How to Solve It is a book describing methods of problem solving.










Mascheroni Construction with compass alone.







Right Triangles, Formulas and Facts

Mind Map of the Pythagorean Theorem
Proofs by shears, translation, similarity. Facts.

Brahmagupta Formula Extension Area of any quadrilateral.


Brahmagupta's Theorem Cyclic quadrilateral.

Brahmagupta's Corollary Cyclic quadrilateral.

Brahmagupta's Formula  Area of a cyclic quadrilateral.


Most Popular Videos of Geometry

Proposed Problem 50,
49, 48, 47, 46, 45, 44, 43.

Proposed Problem 42. Angles and triangles.



Sangaku Problem 41. "Mickey Mouse."

Proposed Problem 40.
Triangle, Incenter, Excenter, Angles 80, 40, Distances.

Proposed Problem 40. Geometry Help.


Adams' Circle Theorem

Monge & d'Alembert Three Circles Theorem II with Dynamic Geometry

Miquel's Pentagram with Dynamic Geometry.

Table of Content

  1. Triangles. Theorems and problems about triangles.

  2. Circles. Theorems and problems about circles.

  3. Triangle Centers

  4. Archimedes' Book of Lemmas

  5. Quadrilaterals

  6. Adams' Circle

  7. First Ajima-Malfatti Point

  8. Second Ajima-Malfatti Point

  9. Apollonius' Tangency Problem for Three Circles Illustration with animation and sound.

  10. The Bevan Point

  11. Blanchet Theorem

  12. Butterfly Theorem. See also: Butterfly Theorem Puzzle

  13. Carnot's Theorem

  14. Ceva's Theorem

  15. Clifford's Circles Chain Theorems

  16. Equal Incircles Theorem

  17. Equilic Quadrilateral.

  18. Euler and his beautiful and extraordinary formula that links the 5 fundamental constants e, i, Pi , 1 and 0, together!

  19. Eyeball Theorem. Illustration

  20. Gergonne Point Theorem

  21. Heron's Formula. Key facts and a purely geometric step-by-step proof.

  22. Johnson's Theorem

  23. Kurschak's Tile & Theorem

  24. Langley Problem: 20° Isosceles Triangle Adventitious angles.

  25. Lemoine Theorem Animated Angle

  26. Menelaus' Theorem

  27. Miquel's Pentagram. Proof

  28. Miquel's Pentagram. Dynamic Geometry Cabri, GSP, Cinderella, C.a.R.

  29. Monge & d'Alembert Three Circles Theorem I - Dynamic Geometry Requires Java applet 1.3 or higher.

  30. Monge & d'Alembert Three Circles Theorem II - Dynamic Geometry Requires Java applet 1.3 or higher.

  31. Morley's Theorem

  32. Napoleon's Theorem

  33. Nagel Point Theorem. See also: Nagel Point Flowchart Proof, Nagel Point Puzzle.

  34. Newton's Theorem: Newton's Line

  35. Nine-Point Center, Nine-Point Circle, Euler Line

  36. Parallelogram with Squares theorem.

  37. Pascal's Mystic Hexagram Theorem Proof

  38. Pentagons and Pentagrams. Menelaus and Collinearity

  39. Platonic Solids. Interactive animation.

  40. Poncelet's Theorem

  41. Proposed Problems about congruence of line segments, angles, and triangles. Level: High School, SAT Prep, College geometry.

  42. Ptolemy's Theorem.

  43. Ptolemy's Extension Cyclic Quadrilateral: Ratio of the Diagonals.

  44. Sangaku Problem

  45. Sangaku Problem 2

  46. Sangaku Problem 3

  47. Sawayama -Thebault's theorem

  48. Semiperimeter and excircles of a triangle

  49. Semiperimeter and incircle of a triangle

  50. Semiperimeter, incircle and excircles of a triangle

  51. Seven Circles Theorem

  52. Simson Line

  53. Simson Line: Angle between two Simson lines

  54. Steiner's Theorem

  55. 100° Isosceles Triangle Problem

  56. Triangles

  57. Triangle with the bisectors of the exterior angles. Collinearity

  58. Triangle & squares. 22 theorems, visual illustrations.

  59. Triangle with Squares 0 Two squares.

  60. Triangle with Squares 1 Two squares.

  61. Triangle with Squares 2 Two squares.

  62. Triangle with Squares 3 Three squares.

  63. Triangle with Squares 4 Finsler-Hadwiger Theorem.

  64. Triangle with Squares 5 Two squares, median and altitude.

  65. Triangle with Squares 6 Four squares.

  66. Triangle Centers

  67. Van Aubel's Theorem Quadrilateral with Squares

  68. Generalizing Van Aubel: Michael de Villiers' Theorems.

  69. Varignon and Wittenbauer parallelograms

  70. Adjacent Angles and Five Bisectors



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Last updated: October 13, 2007