MathPlotAI Logo MathPlotAI

Feuerbach Theorem Demonstration

Feuerbach Theorem Demonstration
Loading the math board and drawing, please wait…
2017-10-30 09:04
TriangleCircleGeometric Construction
This example demonstrates Feuerbach's Theorem, which states that the circle passing through the points of tangency of the incircle and excircles of a triangle is tangent to all three circles. It involves core concepts like circles, incircle, excircles, tangency, and geometric constructions. The construction uses GeoGebra commands and objects such as Line, AngularBisector, OrthogonalLine, Intersect, Circle, and Midpoint. Suitable for high school and above mathematics learners to explore the geometric properties and construction methods of the theorem.

GeoGebra Commands & Parameters

  1. Line(A, B) → f
  2. Line(B, C) → g
  3. Line(C, A) → h
  4. AngularBisector(B, A, C) → i
  5. AngularBisector(A, C, B) → j
  6. AngularBisector(A, B, C) → k
  7. OrthogonalLine(A, i) → l
  8. OrthogonalLine(C, j) → m
  9. OrthogonalLine(B, k) → n
  10. Intersect(i, j) → D
  11. Intersect(k, l) → E
  12. Intersect(j, l) → F
  13. Intersect(i, m) → G
  14. OrthogonalLine(F, g) → p
  15. OrthogonalLine(D, g) → q
  16. OrthogonalLine(G, g) → r
  17. OrthogonalLine(E, g) → s
  18. Intersect(g, p) → H
  19. Intersect(g, q) → I
  20. Intersect(g, r) → J
  21. Intersect(g, s) → K
  22. Circle(E, K) → c
  23. Circle(G, J) → d
  24. Circle(D, I) → e
  25. Circle(F, H) → t
  26. Midpoint(A, B) → L
  27. Midpoint(B, C) → M
  28. Midpoint(C, A) → N
  29. Circle(M, N, L) → c_1