Geometrium
1. A new generalization of Bottema's theorem
2. Area of a rhombus
3. Area of a regular convex pentagon
4. A conic inside a hexagon
5. An ellipse inside a heptagon
6. Intersecting circles
7. Concurrent point in an arbitrary triangle
8. A generalization of Droz-Farny line theorem
9. Equal sums of triangle areas
10. A generalization of Thébault's theorem
11. A rhombus inside a parallelogram
12. Square inside a square
13. Equilateral triangle inside an equilateral triangle
14. A concyclic points inside a pentagon
15. Point of concurrency in an arbitrary triangle
16. Point of concurrency in a cyclic pentagon
17. Point of concurrency in a cyclic quadrilateral
18. Congruent triangles inside an arbitrary triangle
19. Two congruent triangles
20. Intersection point of the perpendicular lines
21. Point of intersection of the normals
22. Ratio of the areas of two triangles
23. Segment of altitude equal to the side of the triangle
24. Equal sums of squares of parallelogram line segments
25. Point of concurrency and golden ratio
26. Ratio of areas
27. Perpendicular lines
28. Intersection point of three circles
29. Six points on conic section
30. Six points on an ellipse
31. Six concyclic points
32. An ellipse defined by vertices and orthocenters
33. Intersection point of three circles II
34. Intersection point of three circles III
35. Line segments intersecting at the nine-point center
36. Constant sum of triangle areas
37. Four concyclic points
38. A generalization of Napoleon's theorem
39. A generalization of constant chord theorem
40. Two triangles of equal area
41. An equilateral triangle whose vertices are Fermat points
42. Three concurrent line segments
43. Variations on Napoleon's theorem
44. Concyclic points in the plane of tangential quadrilateral
45. Intersection point of three circles IV
46. A generalization of butterfly theorem
47. Intersecting secants of two congruent circles
48. Tangent-secant theorem for two congruent circles
49. An ellipse determined by circumcenters
50. Three equilateral triangles
51. Characterizations of cyclic quadrilaterals
52. Four concyclic triangle centers
53. Four concyclic triangle centers II
54. Four concyclic triangle centers III
55. Four concyclic triangle centers IV
56. Four concyclic triangle centers V
57. Four concyclic triangle centers VI
58. Five concyclic triangle centers
59. Five concyclic triangle centers II
60. Intersection point of three circles V
61. Seven concyclic triangle centers
62. Three circles related to Conway's circle
63. Points of concurrency of the lines defined by triangle centers and vertices
64. Isosceles triangle and excircle
65. Area of bicentric quadrilateral
66. Area of bicentric pentagon
67. Area of bicentric hexagon
68. Collinearity in bicentric pentagon
69. Collinearity in bicentric hexagon
70. Parallelogram and line
71. Concyclicity in bicentric pentagon
72. Collinearity in tangential pentagon
73. Four orthocenters lie on a circle
74. Five orthocenters lie on a circle
75. Six orthocenters lie on a circle
76. Eight orthocenters lie on a circle
77. Collinearity in bicentric pentagon II
78. Six conelliptic points
79. Triangle and line
80. Parallelogram and line II
81. A variation on a theorem of Viviani
82. A variation on a theorem of Morley
83. Ratio of area of triangle and hexagon
84. Ratio of area of triangle and hexagon II
85. Collinearity in bicentric heptagon
86. Collinearity in bicentric octagon
87. Equal sums of line segments
88. Equal products of triangle areas
89. Three pairs of similar triangles
90. Four pairs of similar triangles
91. Principal diagonals of octagon meet in a single point
92. Constant product of the lengths of two line segments
93. A property of equilateral triangle
94. Sum of areas of triangles
95. An identity for bicentric quadrilateral