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Rotating Circle and Locus

Rotating Circle and Locus
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2017-06-09 03:36
CircleTransformationLocus
This example demonstrates the concept of rotating circles and loci. Key mathematical concepts include circles, rotation, and loci. Using GeoGebra commands such as Circle, Rotate, Ray, etc., dynamic geometric figures can be constructed. Suitable for high school geometry and calculus courses.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Point(c) → C
  3. Line(C, A) → f
  4. Intersect(c, f, 2) → D
  5. Rotate(D, ((-a) * π / 180), C) → D'
  6. Ray(C, D') → g
  7. Point(g) → E
  8. Midpoint(D, E) → F
  9. Line(F, D) → i
  10. OrthogonalLine(D, i) → j
  11. Intersect(c, j) → J, K
  12. CircleArc(A, K, D) → k
  13. Angle(D, C, D') → α
  14. Circle(F, E) → d
  15. Point(k) → G
  16. CircleArc(A, C, D) → e
  17. Ray(D, G) → h
  18. Intersect(d, h, 2) → H
  19. Midpoint(C, E) → I
  20. Distance(G, I) → distanceGI
  21. Distance(H, I) → distanceHI
  22. Polygon(C, E, D) → poly1, d_1, c_1, e_1
  23. Intersect(d, h) → L, M
  24. Distance(I, G) → distanceIG
  25. Distance(I, L) → distanceIL
  26. Segment(D, E) → l
  27. Dilate(C, If[0 < b ≤ 1, 1 - b, 0], I) → C'
  28. Segment(C, C') → m
  29. Rotate(C, If[1 < b ≤ 2, ((-(b - 1)) * π), (-π)], I) → C'_1
  30. Rotate(C', If[1 < b ≤ 2, ((-(b - 1)) * π), (-π)], I) → C''
  31. Segment(C'_1, C'') → m'
  32. Dilate(D, If[2 < b ≤ 3, 3 - b, 0], G) → D'_1
  33. Dilate(G, If[3 < b ≤ 4, 4 - b, 0], L) → G'
  34. Segment(D, D'_1) → n
  35. Segment(G, G') → p
  36. Line(D, G) → q
  37. Intersect(d, q) → N, O
  38. Distance(D, G) → o
  39. Distance(D, O) → r
  40. Dilate(D, If[2 < b ≤ 3, 3 - b, 0], L) → D'_2
  41. Segment(D, D'_2) → s
  42. Dilate(L, If[3 < b ≤ 4, 4 - b, 0], G) → L'
  43. Segment(L, L') → t
  44. Dilate(I, If[4 < b ≤ 5, 5 - b, 0], G) → I'
  45. Segment(I, I') → f_1
  46. Angle(L, I, G) → β
  47. Rotate(I, If[5 < b ≤ 6, ((-(b - 5)) * β), (-β)], I) → I'_1
  48. Rotate(I', If[5 < b ≤ 6, ((-(b - 5)) * β), (-β)], I) → I''
  49. Segment(I'_1, I'') → g_1
  50. Segment(C, D) → h_1