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Orthopole, Wallace-Simpson Line, and Deltoid

Orthopole, Wallace-Simpson Line, and Deltoid
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2017-08-20 08:18
TransformationGeometric ConstructionLocus
This example illustrates the geometric relationships between the orthopole, Wallace-Simpson line, and deltoid. Key mathematical concepts include orthogonal lines, poles, medians of a triangle, and similarity transformations. By drawing the sides of a triangle, constructing medians, using the concept of orthogonal lines and poles, and tracing the locus, the generation of the deltoid is demonstrated. Suitable for high school geometry learners and math enthusiasts.

GeoGebra Commands & Parameters

  1. Line(A, B) → f
  2. Line(B, C) → g
  3. Line(C, A) → h
  4. Circle(A, B, C) → c
  5. Point(c) → D
  6. Tangent(D, c) → i,
  7. OrthogonalLine(A, i) → j
  8. OrthogonalLine(B, i) → k
  9. OrthogonalLine(C, i) → l
  10. Intersect(i, j) → E
  11. Intersect(i, l) → F
  12. Intersect(i, k) → G
  13. OrthogonalLine(E, g) → m
  14. OrthogonalLine(F, f) → n
  15. OrthogonalLine(G, h) → p
  16. Intersect(m, n) → H
  17. Locus(H, D) → loc1
  18. OrthogonalLine(D, g) → q
  19. OrthogonalLine(D, h) → r
  20. OrthogonalLine(D, f) → s
  21. Intersect(f, s) → I
  22. Intersect(r, h) → J
  23. Intersect(q, g) → K
  24. Line(I, K) → t
  25. Line(K, J) → a