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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Copyright © 1996-2018 Alexander Bogomolny

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