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9-Point Circle Exploration

9-Point Circle Exploration
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2015-08-16 11:19
TriangleCircleGeometric Construction
This example demonstrates the properties of the 9-point circle for any triangle through an interactive visual. Key math concepts include triangle, circle, midpoint, foot of altitude, circumcenter, centroid, orthocenter, etc. Construction involves commands like Segment, Midpoint, OrthogonalLine, Intersect, Circle, Center. Suitable for high school geometry instruction to explore the 9-point circle theorem and related properties.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Segment(B, C) → b
  3. Segment(C, A) → c
  4. Midpoint(c) → E_1
  5. Midpoint(b) → F_1
  6. Midpoint(a) → G_1
  7. OrthogonalLine(C, a) → l
  8. OrthogonalLine(A, b) → m
  9. OrthogonalLine(B, c) → n
  10. Intersect(l, m) → I_1
  11. Intersect(l, a) → G
  12. Intersect(n, c) → I
  13. Intersect(m, b) → H
  14. Midpoint(a) → D
  15. Midpoint(c) → F
  16. Midpoint(b) → E
  17. Midpoint(I_1, A) → L
  18. Midpoint(I_1, B) → J
  19. Midpoint(I_1, C) → K
  20. Circle(D, J, E) → d
  21. Center(d) → R
  22. Angle(a, l) → α
  23. Angle(b, m) → β
  24. Angle(c, n) → γ
  25. Segment(A, L) → e
  26. Segment(L, I_1) → f
  27. Segment(C, K) → g
  28. Segment(K, I_1) → h
  29. Segment(B, J) → i
  30. Segment(J, I_1) → j
  31. Line(B, I) → k
  32. LineBisector(c) → q
  33. LineBisector(b) → r
  34. LineBisector(a) → p
  35. Intersect(q, r) → M
  36. Angle(c, q) → δ
  37. Angle(a, p) → ε
  38. Angle(b, r) → ζ
  39. Segment(C, D) → s
  40. Segment(B, F) → t
  41. Intersect(s, t) → N
  42. Segment(A, E) → a_1
  43. AngularBisector(c, a) → b_1, c_1
  44. AngularBisector(c, b) → d_1, e_1
  45. AngularBisector(b, a) → f_1, g_1
  46. Intersect(c_1, e_1) → O
  47. OrthogonalLine(O, a) → h_1
  48. Intersect(h_1, a) → P
  49. Circle(O, P) → k_1