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Special Points and Lines in a Triangle by Ricardo García Mesa

Special Points and Lines in a Triangle by Ricardo García Mesa
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2013-03-25 20:34
TriangleCoordinate GeometryGeometric Construction
This applet demonstrates some special points and lines in a triangle, such as the centroid and orthocenter. Using GeoGebra commands like Polygon, Midpoint, and Segment, it provides a visual understanding of these geometric concepts. Suitable for students in middle school and above.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → polígono1, c, a, b
  2. Midpoint(c) → D
  3. Midpoint(b) → E
  4. Midpoint(a) → F
  5. Segment(D, C) → d
  6. Segment(E, B) → e
  7. Segment(F, A) → f
  8. Intersect(d, e) → G
  9. AngularBisector(a, b) → j, k
  10. AngularBisector(a, c) → l, m
  11. AngularBisector(c, a) → n, p
  12. AngularBisector(b, c) → q, r
  13. Intersect(k, p) → H
  14. OrthogonalLine(B, b) → t
  15. OrthogonalLine(A, a) → a_1
  16. OrthogonalLine(C, c) → b_1
  17. Intersect(t, a_1) → I
  18. OrthogonalLine(D, c) → c_1
  19. OrthogonalLine(E, b) → d_1
  20. OrthogonalLine(F, a) → e_1
  21. Intersect(c_1, d_1) → J
  22. Circle(J, A) → f_1
  23. OrthogonalLine(H, c) → h_1
  24. Intersect(h_1, c) → K
  25. Circle(H, K) → k_1
  26. Line(I, J) → j_1
  27. Polygon(L, M, N, O) → polígono2, l_2, m_1, n_1, o_1
  28. Polygon(P, Q, R, S) → polígono3, p_1, q_1, r_1, s_1

AI Drawing Prompt Reference

Draw a triangle ABC, then draw the medians DE, EF, and FD, find the orthocenter G, draw the angle bisectors j and k, and l and m, then find the incenter H, draw the altitudes from A, B, and C to the opposite sides t, a1, and b1, find their intersection I, draw the perpendiculars from D, E, and F to the opposite sides c1, d1, and e1, find their intersection J, draw a circle with center J and radius A, draw the perpendicular bisector of H and K, find their intersection K, draw a circle with center H and radius K, and finally draw the line through I and J.
The prompt above was compiled from the original drawing commands and is for reference only.