MathPlotAI Logo MathPlotAI

Pedal Circle of Isogonal Conjugates

Pedal Circle of Isogonal Conjugates
Loading the math board and drawing, please wait…
2015-02-14 05:39
TriangleCircleGeometric Construction
In collections A Tour of Triangle Geometry
This example demonstrates the pedal circle of isogonal conjugates. The pedal circle is formed by the feet of the perpendiculars dropped from an arbitrary point to the sides (possibly extended) of a triangle. Commands used include Segment, Mirror, Circle, Center, Midpoint, Line, OrthogonalLine, and Intersect. Suitable for high school geometry students and math enthusiasts.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Segment(B, C) → b
  3. Segment(C, A) → c
  4. Mirror(P, c) → P'_3
  5. Mirror(P, a) → P'_1
  6. Mirror(P, b) → P'_2
  7. Circle(P'_3, P'_1, P'_2) → d
  8. Center(d) → Q
  9. Mirror(Q, c) → Q'_3
  10. Mirror(Q, a) → Q'_1
  11. Mirror(Q, b) → Q'_2
  12. Circle(Q'_1, Q'_3, Q'_2) → g
  13. Midpoint(Q, P) → J
  14. Segment(Q, P) → l
  15. Line(A, B) → m
  16. Line(C, A) → n
  17. Line(B, C) → q
  18. OrthogonalLine(Q, q) → e
  19. OrthogonalLine(P, q) → f
  20. OrthogonalLine(Q, m) → h
  21. OrthogonalLine(P, m) → i
  22. OrthogonalLine(P, n) → j
  23. OrthogonalLine(Q, n) → k
  24. Intersect(m, i) → D
  25. Intersect(h, m) → E
  26. Intersect(q, e) → F
  27. Intersect(q, f) → G
  28. Intersect(j, n) → H
  29. Intersect(k, n) → I
  30. Circle(D, H, F) → p