两相切圆与公切线中的几何平均动态关系（GoGeometry 第86题）

GeoGebra 命令及参数

1. Circle(A, B) → c
2. Point(c) → C
3. Segment(A, C) → f
4. Line(A, C) → g
5. Circle(C, 2) → d
6. Intersect(d, g, 2) → E
7. Ray(C, E) → h
8. Point(h) → F
9. Circle(F, C) → e
10. Tangent(c, e) → i, j, k, l
11. Intersect(-2.3471111943866765x² - 0.7116767516501961x y + 0.9621700797027014y² + 23.938748022851275x - 0.2856770767977977y = 52.59818359165294, c) → , , ,
12. Intersect(c, i) → D
13. Intersect(e, i) → G
14. Semicircle(A, F) → p
15. Line(A, F) → m
16. OrthogonalLine(C, m) → n
17. Intersect(p, n, 1) → H
18. Segment(C, H) → q
19. Segment(D, G) → r
20. Midpoint(D, G) → I
21. Dilate(A, If[2 < o ≤ 3, 3 - o, 0], D) → A'
22. Dilate(F, If[2 < o ≤ 3, 3 - o, 0], G) → F'
23. Segment(A, A') → s
24. Segment(F, F') → t
25. Dilate(D, If[0 < o ≤ 1, 1 - o, 0], I) → D'
26. Dilate(I, If[1 < o ≤ 2, 2 - o, 0], G) → I'
27. Segment(D, D') → f_1
28. Segment(I, I') → g_1
29. Angle(I, D, A) → α
30. Angle(F, G, I) → β
31. Dilate(A, If[3 < o ≤ 4, 4 - o, 0], C) → A'_1
32. Dilate(C, If[4 < o ≤ 5, 5 - o, 0], F) → C'
33. Segment(A, A'_1) → h_1
34. Segment(C, C') → i_1
35. Rotate(F, If[5 < o ≤ 6, ((o - 5) * π), π], Midpoint[A, F]) → F'_1
36. Midpoint(A, F) → J
37. CircleArc(J, F, F'_1) → c_1
38. Dilate(H, If[7 < o ≤ 8, 8 - o, 0], C) → H'
39. Segment(H, H') → j_1
40. Angle(H, C, A) → γ
41. Segment(F, G) → k_1
42. Angle(H, I, D) → δ
43. Rotate(H, If[9 < o ≤ 10, ((o - 9) * δ), δ], C) → H'_1
44. Rotate(H', If[9 < o ≤ 10, ((o - 9) * δ), δ], C) → H''
45. Segment(H'_1, H'') → l_1
46. Dilate(C, If[10 < o ≤ 11, 11 - o, 0], I) → C'_1
47. Vector(C, C'_1) → u
48. Translate(H'_1, u) → K
49. Translate(H'', u) → H'''
50. Segment(K, H''') → m_1
51. Rotate(K, If[11 < o ≤ 12, ((-(o - 11)) * π), (-π)], I) → K'
52. Rotate(H''', If[11 < o ≤ 12, ((-(o - 11)) * π), (-π)], I) → L
53. Segment(K', L) → n_1