Geometric Problems by Reflection

Below is a list of problems either defined in terms of reflections or for which there is a solution exploiting the reflection transformation.

1. 6 to 9 Point Circle: What Is It About?
2. A Circle-Stacking Theorem
3. A Problem of Hinged Squares
4. A Property of the Line IO
5. A Property of the Line IO: A Proof From The Book
6. A Quadrilateral With Equal Opposite Sides And Angles
7. Bisecting Arcs
8. Bisection of Yin and Yang
9. Butterfly theorem
10. Ceva's Theorem
11. Chords, Concurrency and Orthic Triangle
12. Classification of Quadrilaterals
13. Construction of n-gon by midpoints of its edges
14. Cyclic Incenters
15. Droz-Farny Line Theorem
16. Fagnano's Problem
17. Fagnano's Problem in Reverse
18. Fermat Point and Generalizations
19. Fixed Point of Circles Orthogonal to the Given One
20. Golden Ratio in a Irregular Pentagon, Construction I
21. Heron's Problem
22. Internal Tangents to Three Circles
23. Is X a Midpoint of a Chord?
24. Morley's Pursuit of Incidence
25. Orthocenter and Three Equal Circles
26. Pinning Butterfly on Radical Axes
27. Problem of Equal Steps II
28. Reflections of a Line Through the Orthocenter
29. Reflections of a Point on the Circumcircle
30. Reflections of the Orthocenter
31. Reflections in Ellipse
32. Simson line
33. Solution VI by Tom Verhoeff
34. Symmedian and Antiparallel
35. Synthetic proof of Christopher Bradley's Conjecture
36. The 80-80-20 Triangle Problem, A Variant
37. The 80-80-20 Triangle Problem, Solution #2
38. The Broken Chord Theorem by Paper Folding
39. The Euler Line
40. The Eyeball Theorem
41. Three Congruent Circles by Reflection
42. Three Congruent Circles by Reflection II
43. Three Congruent Circles by Reflection III
44. Three Parallels in a Triangle
45. Two Butterflies Theorem
46. Two Congruent Circles by Reflection
47. Two Triangles With Common Base and Altitude
48. Zaslavsky's Theorem

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