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Circumcenter of the Tangential Triangle

Circumcenter of the Tangential Triangle
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2015-02-14 09:27
TriangleCircleCoordinate GeometryGeometric Construction
In collections A Tour of Triangle Geometry
This example demonstrates that the circumcenter of the tangential triangle lies on the Euler Line. Key concepts include triangles, circles, and the Euler Line. Using GeoGebra commands such as Line, Midpoint, Segment, Intersect, Mirror, Circle, Center, etc., the tangential triangle and its circumcenter are constructed. Suitable for high school geometry education.

GeoGebra Commands & Parameters

  1. Line(A, B) → a
  2. Line(B, C) → b
  3. Line(C, A) → c
  4. Midpoint(B, A) → D
  5. Midpoint(A, C) → E
  6. Midpoint(C, B) → F
  7. Segment(A, F) → d
  8. Segment(D, C) → e
  9. Segment(E, B) → f
  10. Intersect(d, e) → G
  11. Mirror(G, c) → G'_3
  12. Mirror(G, a) → G'_1
  13. Mirror(G, b) → G'_2
  14. Circle(G'_1, G'_3, G'_2) → g
  15. Center(g) → K
  16. Ray(A, K) → h
  17. Angle(G, A, E) → α
  18. Angle(B, A, K) → β
  19. Circle(A, C, B) → k
  20. Tangent(A, k) → i,
  21. Tangent(B, k) → j,
  22. Tangent(C, k) → l,
  23. Intersect(i, j) → C'
  24. Intersect(i, l) → B'
  25. Intersect(j, l) → A'
  26. Polygon(C', B', A') → poly1, j_1, h_1, i_1
  27. Circle(B', C', A') → q
  28. Center(k) → O
  29. OrthogonalLine(A, b) → m
  30. OrthogonalLine(C, a) → n
  31. Intersect(m, n) → H
  32. Line(H, O) → p
  33. Center(q) → J
  34. Mirror(H, O) → L
  35. Midpoint(H, O) → N