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Demonstration of Orthocenter by Alexi

Demonstration of Orthocenter by Alexi
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2016-10-18 11:15
TriangleAngleGeometric Construction
This example demonstrates how to construct the orthocenter of a triangle using GeoGebra commands, involving perpendiculars, midpoints, circle intersections, and angles. Core mathematical concepts include triangle geometry and geometric constructions. Key GeoGebra commands and objects used are Segment, Midpoint, Circle, Intersect, Point, and Angle, as listed in the construction summary. Suitable for high school mathematics education to understand orthocenter properties and geometric construction techniques.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Segment(B, C) → g
  3. Segment(A, C) → h
  4. Midpoint(f) → D
  5. Circle(D, B) → c
  6. Segment(A_1, B_1) → f_3
  7. Midpoint(f_3) → D_3
  8. Circle(D_3, B_1) → c_3
  9. Intersect(c_3, h, 1) → E
  10. Segment(A_1, B_1) → f_1
  11. Midpoint(f_1) → D_1
  12. Circle(D_1, B_1) → c_1
  13. Intersect(c_1, g, 1) → F
  14. Segment(A_3, B_3) → f_4
  15. Midpoint(f_4) → D_4
  16. Circle(D_4, B_3) → c_4
  17. Segment(A_4, B_4) → f_5
  18. Midpoint(f_5) → D_5
  19. Circle(D_5, B_4) → c_5
  20. Intersect(c_4, h, 1) → H
  21. Intersect(c_5, g, 1) → I
  22. Point(h) → G
  23. Circle(A, G) → d
  24. Segment(A_5, C_1) → h_1
  25. Point(h_1) → G_1
  26. Circle(A_5, G_1) → d_1
  27. Intersect(d, d_1, 1) → J
  28. Segment(J, B) → i
  29. Point(g) → K
  30. Circle(B, K) → e
  31. Segment(A_6, C_2) → h_2
  32. Point(h_2) → G_2
  33. Circle(A_6, G_2) → d_2
  34. Intersect(d, d_2, 1) → L
  35. Segment(L, B) → j
  36. Segment(B_5, C_2) → g_1
  37. Point(g_1) → K_1
  38. Circle(B_5, K_1) → e_1
  39. Intersect(e, e_1, 2) → M
  40. Segment(M, A) → k
  41. Segment(A, M) → l
  42. Segment(L, B) → m
  43. Intersect(d_2, j, 2) → N
  44. Angle(A, C, B) → α

AI Drawing Prompt Reference

Draw a triangle and construct its orthocenter. Start by drawing the three sides of the triangle. For each side, find its midpoint and draw a circle centered at that midpoint passing through one endpoint; the circle intersects the opposite side at a foot of the altitude. Then, on one side, pick an arbitrary point and draw a circle with that point as radius; on another side, pick another point and draw another circle; the two circles intersect at a point, which you connect to the third vertex to form an altitude. Repeat similarly to construct the other two altitudes. The three altitudes meet at the orthocenter. Finally, mark one interior angle of the triangle.
The prompt above was compiled from the original drawing commands and is for reference only.