A Tour of Triangle Geometry

Steve Phelps, Feb 11, 2015

Inspired by Paul Yiu


  • 1. Orthocenter and Circumcenter are Isogonal
  • 2. The Incenter, Gergonne Point, and Tritangent Circles
  • 3. The Excircles and the Nagel Point
  • 4. The Excircles and the Nagel Point 2
  • 5. The Symmedian Point
  • 6. Constructing Isogonal Conjugates
  • 7. Pedal Circle of Isogonal Conjugates
  • 8. The Orthocenter and CIrcumcenter are Isogonal Conjugates
  • 9. The Nine-Point Circle and the Euler Line
  • 10. The Feuerbach Theorem and the Feuerbach Point
  • 11. The Feuerbach Theorem and the Feuerbach Point Part 2
  • 12. The Symmedian Point is Isogonal Conjugate of Centroid
  • 13. The Symmedian Point and the Tangential Triangle
  • 14. Circumcenter of the Tangential Triangle
  • 15. Incenter is the Isogonal Conjugate of Itself.
  • 16. The Gergonne Point and Intouch Triangle
  • 17. Isongonal Conjugate of the Gergonne Point
  • 18. The Nagel Point and the Extouch Triangle
  • 19. Gergonne Point, Nagel Point, and Isotomic Conjugates
  • 20. The Isogonal Conjugate of a Point on the Circumcircle
  • 21. Another Way To Find The Isogonal Conjugate
  • 22. Isotomic Conjugate of Point at Infinity and Steiner Ellipse
  • 23. The Wallace-Simson Line
  • 24. Reflecting a Point on the Circumcircle
  • 25. Wallace-Simson Lines of Antipodal Points
  • 26. The Refelctions of a Line Through the Orthocenter
  • 27. The Euler Reflection Point
  • 28. A Line Through the Circumenter.
  • 29. Isogonal Conjugate of Line Through the Circumcenter
  • 30. The Isogonal Conjugate of a Line
  • 31. The Jarebek Hyperbola - Isogonal Conjugate of the Euler Line
  • 32. Isogonal Conjugate Fun
  • 33. More About the Jerabek Hyperbola
  • 34. The Kiepert Hyperbola and the Brocard Axis
  • 35. The Center of the Kiepert Hyperbola
  • 36. The Feuerbach Hyperbola
  • 37. Pedal Circles of Points on Feuerbach Hyperbola
  • 38. The Stammler Hyperbola
  • 39. A Circumconic with Given Center
  • 40. The Steiner Circumellipse
  • 41. The Steiner Point
  • 42. The Fourth Intersection Point of the Circumconic
  • 43. Conics Through the Traces of Two Points
  • 44. The Hyperbola C(P,G) Where P is on Circumcircle
  • 45. The Central Conic Cevian Complement
  • 46. The Central Conic Cevian Complement of the Incenter
  • 47. The Central Conic Cevian Complement of the Symmedian Point
  • 48. Isongonal Conjugates are Foci of Inscribed Ellipse
  • 49. The Inscribed Ellipse with Foci H and O and Center N.
  • 50. The Inscribed Conic with Symmedian as Center
  • 51. Inscribed Parabola
  • 52. The Perspector of the Inscribed Parabola
  • 53. Exeter Point as Focus of Inscribed Parabola
  • 54. The Reflection Conjugate r(P)
  • 55. P and r(P) lie on Rectangular Circum-Hyperbola
  • 56. Collinear Points, Reflection Points, Circum-Hyperbola
  • 57. Reflections of the Orthocenter in Cevian Lines
  • 58. Isogonal Conjugate of the Nine-Point Center
  • 59. The Reflection Triangle and Collinear Points
  • 60. The Reflection Triangle and the Orthocenter
  • 61. The Reflection Triangle in Perspective and the Nueberg Cubic
  • 62. Reflection Triangle for Points on Euler Line

1.

Orthocenter and Circumcenter are Isogonal

The classical centers are centroid, the circumcenter, the orthocenter and the incenter. The orthocenter (H) and the circumcenter (O) are shown below. The line AH and AO are isogonal with respect to sides AB and AC. Go ahead and draw lines BH and BO as well as CH and CO. Confirm that they are isogonal.
– Steve Phelps

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