Table of Content

1. Triangles. Theorems and problems about triangles.

2. Circles. Theorems and problems about circles.

3. Triangle Centers

4. Arbelos, Inscribed Circle and Concyclic Points Cyclic Quadrilateral.

5. Archimedes' Book of Lemmas

6. Quadrilaterals

7. Adams' Circle

8. First Ajima-Malfatti Point

9. Second Ajima-Malfatti Point

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

11. The Bevan Point

12. Blanchet Theorem

13. Butterfly Theorem. See also: Butterfly Theorem Puzzle

14. Carnot's Theorem

15. Ceva's Theorem

16. Clifford's Circles Chain Theorems

17. Equal Incircles Theorem

18. Equilic Quadrilateral.

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

20. Eyeball Theorem. Illustration

21. Four Circles Theorem

22. Gergonne Point Theorem

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

24. ncenter, Excenter, Incircle, Excircle

25. Isogonic-Jacobi Theorem

26. Johnson's Theorem

27. Kurschak's Tile & Theorem

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

29. Lemoine Theorem Animated Angle

30. Marion Walter's Theorem

31. Mascheroni Construction

32. Menelaus' Theorem

33. Miquel's Pentagram. Proof

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

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

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

37. Morley's Theorem

38. Napoleon's Theorem

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

40. Newton's Theorem: Newton's Line

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

42. Orthopole of a Triangle: Using TracenPoche Dynamic Geometry Software

43. Parallelogram with Squares theorem.

44. Pascal's Mystic Hexagram Theorem Proof

45. Pentagons and Pentagrams. Menelaus and Collinearity

46. Platonic Solids. Interactive animation.

47. Poncelet's Theorem

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

49. Ptolemy's Theorem.

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

51. Sangaku Problem

52. Sangaku Problem 2

53. Sangaku Problem 3

54. Sawayama -Thebault's theorem

55. Semiperimeter and excircles of a triangle

56. Semiperimeter and incircle of a triangle

57. Semiperimeter, incircle and excircles of a triangle

58. Seven Circles Theorem

59. Simson Line

60. Simson Line: Angle between two Simson lines

61. Steiner's Theorem

62. 100° Isosceles Triangle Problem

63. Taylor Circle Theorem

64. Three Circles Theorem

65. Three Tangent Circles Theorem

66. Triangles

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

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

69. Triangle with Squares 0 Two squares.

70. Triangle with Squares 1 Two squares.

71. Triangle with Squares 2 Two squares.

72. Triangle with Squares 3 Three squares.

73. Triangle with Squares 4 Finsler-Hadwiger Theorem.

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

75. Triangle with Squares 6 Four squares.

76. Triangle Centers

77. Van Aubel's Theorem Quadrilateral with Squares

78. Van Aubel's Theorem II: Triangle and Cevians

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

80. Varignon and Wittenbauer parallelograms

81. Adjacent Angles and Five Bisectors

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