List R-P
Roles of a Point.
The "Discoverer" database version: October 2013.
Last update: 2014-03-22

The Complement of the Center of the Brocard Circle is the
  1. Center of the Brocard Circle of the Medial Triangle.
  2. Nine-Point Center of the First Brocard Triangle.
  3. Center of the Brocard Circle of the Half-Anticevian Triangle of the Centroid.
  4. Circumcenter of the First Brocard Triangle of the Medial Triangle.
  5. Circumcenter of the Second Brocard Triangle of the Medial Triangle.
  6. Circumcenter of the Orthic Triangle of the First Brocard Triangle.
  7. Circumcenter of the Euler Triangle of the First Brocard Triangle.
  8. Nine-Point Center of the Fuhrmann Triangle of the First Brocard Triangle.
  9. Nine-Point Center of the Johnson Triangle of the First Brocard Triangle.
  10. Orthocenter of the Half-Median Triangle of the First Brocard Triangle.
  11. Symmedian Point of the Johnson Triangle of the Half-Median Triangle.
  12. Retrocenter of the Euler Triangle of the Half-Median Triangle.
  13. Center of the Brocard Circle of the Half-Median Triangle of the Antimedial Triangle.
  14. Perspector and Homothetic Center of the Half-Median Triangle and the Triangle of the Circumcenters of the Pedal Corner Triangles of the Center of the Brocard Circle.
  15. Perspector and Homothetic Center of Triangle ABC and the Triangle of the Orthocenters of the Antipedal Corner Triangles of the Center of the Brocard Circle.
  16. Midpoint of the Nine-Point Center and the Symmedian Point of the Medial Triangle.
  17. Midpoint of the Center of the Brocard Circle and the Reflection of the Symmedian Point in the Nine-Point Center.
  18. Image of the Centroid under the Homothety with Center at the Center of the Brocard Circle and Ratio 3/2.
  19. Image of the Midpoint of the Orthocenter and the Symmedian Point under the Homothety with Center at the Nine-Point Center and Ratio -1/2.
  20. Image of the Symmedian Point of the Medial Triangle under the Homothety with Center at the Nine-Point Center and Ratio 1/2.
  21. Kosnita Product of the Reflection of the Symmedian Point in the Nine-Point Center and the Centroid (Homothetic Center).
  22. Anticevian Corner Product of the Centroid and the Center of the Brocard Circle (Homothetic Center).
  23. Antipedal Corner Product of the Orthocenter and the Center of the Brocard Circle (Homothetic Center).
  24. Antipedal Corner Product of the Center of the Brocard Circle and the Orthocenter (Homothetic Center).
  25. Center of the Lemoine Circle of the Medial Triangle.
  26. Center of the Nine-Point Circle of the First Brocard Triangle.
  27. Center of the Brocard Circle of the Half-Median Triangle of the Antimedial Triangle.
  28. Center of the Lemoine Circle of the Half-Median Triangle of the Antimedial Triangle.
  29. Center of the Circumcircle of the Orthic Triangle of the First Brocard Triangle.
  30. Center of the Circumcircle of the Euler Triangle of the First Brocard Triangle.
  31. Center of the Nine-Point Circle of the Fuhrmann Triangle of the First Brocard Triangle.
  32. Center of the Nine-Point Circle of the Johnson Triangle of the First Brocard Triangle.
  33. Center of the Antimedial Circle of the Half-Median Triangle of the First Brocard Triangle.
  34. Center of the Cosine Circle of the Johnson Triangle of the Half-Median Triangle.
  35. Center of the Inverse Circle of the Tangential Circle of the First Brocard Triangle in the Brocard Circle.

    36. The Complement of the Center of the Brocard Circle lies on the

  36. Line through the Centroid and the Tarry Point.
  37. Line through the Outer Napoleon Point and the Symmedian Point.
  38. Line through the Circumcenter and the Reflection of the Symmedian Point in the Orthocenter.
  39. Line through the Nine-Point Center and the Midpoint of the Orthocenter and the Symmedian Point.
  40. Line through the Retrocenter and the Harmonic Conjugate of the Orthocenter with respect to the Centroid and the Nine-Point Center (the Orthocenter is not between the Centroid and Nine-Point Center).
  41. Line through the Center of the Orthocentroidal Circle and the Reflection of the Symmedian Point in the Circumcenter.
  42. Line through the Midpoint of the Centroid and the Nine-Point Center and the Midpoint of the Nine-Point Center and the Symmedian Point.
  43. Line through the Midpoint of the Centroid and the Symmedian Point and the Reflection of the Nine-Point Center in the Symmedian Point.
  44. Line through the Reflection of the Circumcenter in the Symmedian Point and the Reflection of the Symmedian Point in the Centroid.

    45. The Complement of the Center of the Brocard Circle lies on the

  45. Lester Circle of the First Brocard Triangle.
  46. Brocard Circle of the First Brocard Triangle of the Medial Triangle.
  47. Lester Circle of the First Brocard Triangle of the Medial Triangle.
  48. Brocard Circle of the Second Brocard Triangle of the Medial Triangle.
  49. Lester Circle of the Second Brocard Triangle of the Medial Triangle.
  50. Brocard Circle of the Orthic Triangle of the First Brocard Triangle.
  51. Lester Circle of the Orthic Triangle of the First Brocard Triangle.
  52. Brocard Circle of the Euler Triangle of the First Brocard Triangle.
  53. Lester Circle of the Euler Triangle of the First Brocard Triangle.
  54. Lester Circle of the Fuhrmann Triangle of the First Brocard Triangle.
  55. Lester Circle of the Johnson Triangle of the First Brocard Triangle.
  56. Orthocentroidal Circle of the Half-Median Triangle of the First Brocard Triangle.
  57. Brocard Circle of the Johnson Triangle of the Half-Median Triangle.
  58. Circle passing through the Circumcenter, Nine-Point Center and Tarry Point.
  59. Image of the Orthocentroidal Circle under the Homothety with Center the Center of the Brocard Circle and Ratio 3/2.
  60. Image of the Parry Circle under the Homothety with Center the Center of the Brocard Circle and Ratio 3/2.