两割线外角交互探究

GeoGebra 命令及参数

1. PointIn(a) → C
2. Semicircle(C, A) → e
3. Semicircle(A, C) → d
4. Circle(A, B) → c
5. Intersect(c, e, 1) → E
6. Intersect(c, d, 1) → D
7. CircleArc(A, E, D) → g
8. CircleArc(A, D, E) → f
9. Point(f) → F
10. Segment(C, F) → i
11. Intersect(g, i, 1) → H
12. CircleArc(A, F, E) → h
13. Point(h) → G
14. Segment(C, G) → j
15. Intersect(g, j, 1) → I
16. CircleArc(A, H, I) → h_2
17. Min({Distance[A, B], Distance[C, H], Distance[C, I]}) → k
18. Circle(A, (0.4 * k)) → p
19. Segment(A, F) → l
20. Segment(A, G) → m
21. Intersect(p, l, 1) → J
22. Segment(A, I) → n
23. Segment(A, H) → q
24. Intersect(p, n, 1) → K
25. Intersect(p, q, 1) → L
26. Dilate(A, If[0 < b ≤ 1, 1 - b, 0], F) → A'
27. Dilate(A, If[0 < b ≤ 1, 1 - b, 0], G) → A'_1
28. Dilate(A, If[0 < b ≤ 1, 1 - b, 0], H) → A'_2
29. Dilate(A, If[0 < b ≤ 1, 1 - b, 0], I) → A'_3
30. Angle(F, C, G) → ε
31. Rotate(J, If[8 < b ≤ 9, ((b - 8) * ε), ε], A) → J'_1
32. Dilate(A, If[10 < b ≤ 11, 11 - b, 0], C) → A'_7
33. Vector(A, A'_7) → u
34. CircleArc(A, F, G) → t_1
35. CircleArc(A, I, H) → c_2
36. CircleArc(A, H, F) → d_2
37. CircleArc(A, G, I) → e_2
38. CircleArc(A, G, F) → f_2
39. Point(h_2) → R
40. Point(f_2) → Q
41. Segment(R, H) → a_1
42. Segment(R, I) → b_1
43. Segment(Q, F) → g_2
44. Segment(Q, G) → i_2
45. Min({Distance[Q, G], Distance[Q, F], Distance[R, F], Distance[R, G], Distance[C, H], Distance[C, I]}) → o
46. Circle(R, (0.5 * o)) → k_2
47. Circle(Q, (0.5 * o)) → p_2
48. Intersect(p_2, g_2, 1) → S
49. Intersect(k_2, b_1, 1) → P
50. Angle(P, R, H) → ζ
51. Angle(S, Q, G) → μ
52. Angle(H, C, I) → κ
53. Dilate(Q, If[0 < b ≤ 1, 1 - b, 0], G) → Q'
54. Dilate(Q, If[0 < b ≤ 1, 1 - b, 0], F) → Q'_1
55. Segment(Q, Q') → s
56. Segment(Q, Q'_1) → t
57. Dilate(R, If[1 < b ≤ 2, 2 - b, 0], H) → R'
58. Dilate(R, If[1 < b ≤ 2, 2 - b, 0], I) → R'_1
59. Segment(R, R') → r
60. Segment(R, R'_1) → f_1
61. Rotate(S, If[2 < b ≤ 3, ((b - 2) * μ), μ], Q) → S'_1
62. Rotate(P, If[3 < b ≤ 4, ((b - 3) * ζ), ζ], R) → P'
63. CircleSector(R, P, P') → c_1
64. CircleSector(Q, S, S'_1) → d_1
65. Dilate(R, If[5 < b ≤ 6, 6 - b, 0], Q) → R'_2
66. Vector(R, R'_2) → v
67. Translate(c_1, v) → e_1
68. Line(Q, r) → g_1
69. Point(g_1) → M
70. Intersect(p_2, i_2) → N,
71. Rotate(N, (-ζ), Q) → N'
72. Angle(M, Q, N) → α
73. Rotate(e_1, If[5 < b ≤ 6, ((b - 5) * α), α], R'_2) → h_1
74. Rotate(S, If[6 < b ≤ 7, ((b - 6) * (μ - ζ)), μ - ζ], Q) → S'
75. CircleSector(Q, S, S') → k_1
76. Midpoint(Q, C) → O
77. Rotate(Q, If[8 < b ≤ 9, ((-(b - 8)) * π), (-π)], O) → Q'_2
78. Vector(Q, Q'_2) → w
79. Translate(k_1, w) → p_1
80. Line(C, t) → i_1
81. Point(i_1) → T
82. Angle(T, C, F) → β
83. Rotate(p_1, If[8 < b ≤ 9, ((-(b - 8)) * ((2 * π) - β)), β - (2 * π)], Q'_2) → q_1
84. CircleArc(A, H, F) → r_1
85. CircleArc(A, G, I) → s_1