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Fermat Points and the Orthocenter

Fermat Points and the Orthocenter
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2017-01-22 22:49
TriangleOptimizationGeometric Construction
This example demonstrates the geometric relationship between Fermat Points and the Orthocenter in a triangle. Core math concepts include Fermat Points, Orthocenter, Optimization Problems, 2D Vectors, and Geometric Construction. It utilizes commands like Line, Polygon, Circle, Midpoint, Center, Mirror, Intersect, and Centroid in GeoGebra. Suitable for high school and above learners to understand special points in triangles and optimization problems.

GeoGebra Commands & Parameters

  1. Line(A, B) → f
  2. Line(B, C) → g
  3. Line(C, A) → h
  4. Polygon(A, B, C) → poly1, c, a, b
  5. Circle(A, B, C) → d
  6. Midpoint(A, B) → D
  7. Midpoint(B, C) → E
  8. Midpoint(C, A) → F_1
  9. Circle(D, F_1, E) → e
  10. Center(d) → O
  11. Center(e) → N
  12. Mirror(O, N) → H
  13. Polygon(C, B, 3) → poly2, i, j, k, G_1
  14. Polygon(B, A, 3) → poly3, l, m, n, I
  15. Line(I, C) → p
  16. Line(G_1, A) → q
  17. Intersect(p, q) → F_2
  18. Polygon(A, B, 3) → poly4, r, s, t, K
  19. Polygon(B, C, 3) → poly5, f_1, g_1, h_1, L
  20. Line(A, L) → i_1
  21. Line(K, C) → j_1
  22. Intersect(i_1, j_1) → F
  23. Circle(F, F_2, N) → c_1
  24. Line(H, O) → k_1
  25. Centroid(poly1) → G
  26. Midpoint(H, G) → J
  27. Circle(J, G) → d_1
  28. Circle(F, F_2, H) → e_1