任意三角形内切圆中角关系的动态探究（GoGeometry 行动78）

GeoGebra 命令及参数

1. Segment(A, B) → f
2. Rotate(A, (a * π / 180), B) → A'
3. Ray(B, A') → g
4. Point(g) → C
5. Angle(C, A, B) → γ
6. Rotate(C, γ / 2, A) → C'
7. Ray(A, C') → k
8. Segment(C, A) → i
9. Segment(B, C) → h
10. Angle(A, B, A') → α
11. Rotate(A, α / 2, B) → A'_1
12. Ray(B, A'_1) → j
13. Intersect(j, k) → H
14. Segment(H, C) → j_1
15. Segment(A, H) → n
16. OrthogonalLine(H, n) → q
17. Intersect(q, i) → M
18. Segment(H, M) → i_1
19. Circle(B, (0.5 * Min[{f, h, i_1, j_1}])) → c
20. Angle(A, B, A'_1) → β
21. Intersect(c, f, 1) → D
22. Intersect(c, j, 1) → E
23. Angle(C, A, C') → δ
24. Circle(A, Radius[c]) → d
25. Intersect(d, i) → F,
26. Intersect(d, k) → G,
27. OrthogonalLine(H, f) → l
28. OrthogonalLine(H, f) → m
29. Intersect(f, m) → I
30. Angle(H, I, B) → ε
31. Segment(H, C) → p
32. Point(q) → J
33. Angle(J, H, C) → ζ
34. Angle(A, H, J) → η
35. Dilate(B, If[0 < b ≤ 1, 1 - b, 0], H) → B'
36. Segment(B, B') → r
37. Dilate(A, If[1 < b ≤ 2, 2 - b, 0], H) → A'_2
38. Dilate(A, If[1 < b ≤ 2, 2 - b, 0], H) → A'_3
39. Segment(A, A'_3) → s
40. CircleSector(B, D, E) → e
41. CircleSector(A, F, G) → t
42. Rotate(e, If[2 < b ≤ 3, ((b - 2) * β), β], B) → e'
43. Rotate(t, If[3 < b ≤ 4, ((b - 3) * γ / 2), γ / 2], A) → t'
44. Dilate(H, If[4 < b ≤ 5, 5 - b, 0], I) → B'_1
45. Segment(H, B'_1) → f_1
46. Dilate(H, If[5 < b ≤ 6, 6 - b, 0], I) → H'
47. Circle(H, H') → c_1
48. Intersect(c_1, h) → K, O
49. Intersect(c_1, i) → L, N
50. Dilate(H, If[6 < b ≤ 7, 7 - b, 0], C) → H'_1
51. Segment(H, H'_1) → g_1
52. Dilate(M, If[8 < b ≤ 9, 9 - b, 0], H) → M'
53. Segment(M, M') → h_1
54. Line(B, j_1) → k_1
55. Point(k_1) → P
56. Angle(C, B, P) → θ
57. Dilate(B, If[9.5 < b ≤ 10.5, 10.5 - b, 0], H) → B'_2
58. Vector(B, B'_2) → u
59. Translate(e', u) → e''
60. Rotate(e'', If[10.5 < b ≤ 11.5, ((b - 10.5) * θ), θ], H) → e'''
61. Polygon(B, A, C) → poly1, c_2, b_1, a_1