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Soddy Circles

Soddy Circles
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2014-05-08 06:32
CircleCoordinate Geometry
In collections MalinC's GeoGebra-book
This example demonstrates how to construct Soddy circles, which are circles that are tangent to three given circles. The example involves key concepts in circle, geometry, and curve sketching. Using commands such as Polygon, AngularBisector, Intersect, OrthogonalLine, Circle, Line, Angle, the construction of Soddy circles is illustrated. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. AngularBisector(B, A, C) → d
  3. AngularBisector(C, B, A) → e
  4. Intersect(d, e) → D
  5. OrthogonalLine(D, c) → f
  6. Intersect(f, c) → E
  7. Circle(D, E) → g
  8. OrthogonalLine(D, a) → h
  9. Intersect(h, a) → F
  10. OrthogonalLine(D, b) → i
  11. Circle(B, F) → k
  12. Circle(A, E) → p
  13. Circle(C, F) → q
  14. OrthogonalLine(A, a) → j
  15. OrthogonalLine(B, b) → l
  16. OrthogonalLine(C, c) → m
  17. Intersect(q, m) → G, H
  18. Intersect(k, l) → I, J
  19. Intersect(p, j) → K, L
  20. Line(F, K) → n
  21. Line(F, L) → r
  22. Intersect(p, r, 2) → M
  23. Intersect(p, n, 2) → N
  24. Intersect(q, b) → O,
  25. Line(O, I) → s
  26. Intersect(k, s, 2) → P
  27. Line(O, J) → t
  28. Intersect(k, t, 2) → Q
  29. Line(E, G) → a_1
  30. Intersect(q, a_1, 2) → R
  31. Line(E, H) → b_1
  32. Intersect(q, b_1, 2) → S
  33. Circle(M, Q, S) → c_1
  34. Circle(N, P, R) → d_1
  35. Intersect(j, a) → T
  36. Intersect(m, c) → U
  37. Intersect(l, b) → V
  38. Angle(B, T, A) → α
  39. Angle(C, U, A) → β
  40. Angle(B, V, A) → γ

AI Drawing Prompt Reference

Draw three tangent circles and find the intersection of their angle bisectors to get a point. Use this point as the center to draw a circle tangent to one of the given circles. Then, find other intersection points using orthogonal lines and draw two more tangent circles based on these points. Finally, connect some points to form lines and complete the three Soddy circles, showing how they are tangent to the given circles.
The prompt above was compiled from the original drawing commands and is for reference only.