圆内接四边形：证明提示

GeoGebra 命令及参数

1. Circle(A, B) → c
2. Point(c) → C
3. Point(c) → D
4. CircleArc(A, C, D) → d
5. CircleArc(A, D, C) → e
6. Point(e) → E
7. CircleArc(A, D, E) → f
8. CircleArc(A, E, C) → g
9. Point(g) → F
10. Polygon(F, C, D, E) → q1, f_1, c_1, d_1, e_1
11. Segment(C, D) → h
12. Segment(D, E) → i
13. Segment(E, F) → j
14. Ray(F, C) → k
15. Min({i, j, h, Distance[F, C]}) → a
16. Circle(E, (0.2 * a)) → p
17. Intersect(p, j) → G,
18. Angle(F, E, D) → α
19. Rotate(G, If[0 < b ≤ 1, (b * α), α], E) → G'
20. CircleSector(E, G, G') → q
21. Dilate(E, If[1.5 < b ≤ 2.5, 2.5 - b, 0], C) → E'
22. Vector(E, E') → u
23. Translate(q, u) → q'
24. Line(E, k) → l
25. Point(l) → H
26. Angle(G, E, H) → β
27. Circle(C, (0.2 * a)) → r
28. Intersect(r, h, 1) → I
29. Rotate(I, If[0 < b ≤ 1, (b * (π - α)), π - α], C) → I'
30. CircleSector(C, I, I') → s
31. Dilate(A, If[1 < b ≤ 2, 2 - b, 0], D) → A'
32. Dilate(A, If[1 < b ≤ 2, 2 - b, 0], F) → A'_1
33. Segment(A, A') → m
34. Segment(A, A'_1) → n
35. Line(A, i) → t
36. Angle(F, A, D) → γ
37. Rotate(F, γ / 2, A) → F'
38. Angle(F, A, F') → δ
39. Dilate(E, If[2 < b ≤ 3, 3 - b, 0], A) → E'_1
40. Vector(E, E'_1) → v
41. Translate(q, v) → q'_1
42. Point(t) → J
43. Angle(J, A, D) → ε
44. Rotate(q'_1, If[2 < b ≤ 3, ((b - 2) * ε), ε], E'_1) → g_1
45. Dilate(C, If[3 < b ≤ 4, 4 - b, 0], A) → C'
46. Vector(C, C') → w
47. Translate(s, w) → s'
48. Line(A, h) → h_1
49. Point(h_1) → K
50. Angle(D, A, K) → ζ
51. Rotate(s', If[3 < b ≤ 4, ((b - 3) * ((2 * π) - ζ)), (2 * π) - ζ], C') → s''
52. Dilate(A, If[4 < b ≤ 5, 5 - b, 0], F') → A'_2
53. Rotate(D, π - γ / 2, A) → D'
54. Dilate(A, If[4 < b ≤ 5, 5 - b, 0], D') → A'_3
55. Segment(A, A'_2) → i_1
56. Segment(A, A'_3) → j_1
57. Rotate(I, If[4 < b ≤ 5, ((b - 4) * (π - α)), π - α], C) → I'_1
58. Rotate(G, If[4 < b ≤ 5, ((b - 4) * α), α], E) → G'_1
59. CircleSector(C, I, I'_1) → k_1
60. CircleSector(E, G, G'_1) → p_1
61. Dilate(E, If[5.5 < b ≤ 6.5, 6.5 - b, 0], A) → E'_2
62. Vector(E, E'_2) → u_1
63. Translate(p_1, u_1) → q_1
64. Line(A, j) → l_1
65. Point(l_1) → L
66. Angle(F, A, L) → η
67. Rotate(q_1, If[5.5 < b ≤ 6.5, ((b - 5.5) * ((2 * π) - η)), (2 * π) - η], E'_2) → r_1
68. CircleArc(A, F, D) → s_1
69. CircleArc(A, D, F) → t_1
70. CircleArc(A, F, D) → c_2
71. Dilate(C, If[6.5 < b ≤ 7.5, 7.5 - b, 0], A) → C'_1
72. Vector(C, C'_1) → v_1
73. Translate(k_1, v_1) → d_2
74. Line(A, k) → m_1
75. Point(m_1) → M
76. Angle(M, A, F) → θ
77. Rotate(d_2, If[6.5 < b ≤ 7.5, ((b - 6.5) * θ), θ], C'_1) → e_2
78. CircleArc(A, D, F) → f_2
79. Segment(F, C) → n_1