动态几何演示：Antonio Gutierrez 定理

GeoGebra 命令及参数

1. Rotate(A, (-((a * π / 180))), B) → A'
2. Angle(A', B, A) → α
3. Segment(A, B) → f
4. Ray(B, A') → g
5. Point(g) → C
6. Segment(A, C) → h
7. Segment(B, C) → i
8. LineBisector(i) → j
9. LineBisector(f) → k
10. Line(A, B) → m
11. OrthogonalLine(C, m) → n
12. Intersect(m, n) → E
13. Angle(E, C, A) → γ
14. Angle(E, A, C) → ε
15. Dilate(C, If[3 < o ≤ 4, 4 - o, 0], E) → C'_1
16. Dilate(B, If[3 < o ≤ 4, 4 - o, 0], E) → B'
17. Midpoint(A, B) → J
18. Segment(A, E) → g_1
19. Segment(A, J) → h_1
20. Min(f, i) → u
21. Circle(B, (0.2 * u)) → r_1
22. Intersect(r_1, f) → K,
23. Intersect(r_1, i) → L,
24. CircleSector(B, L, K) → s_1
25. Point(f) → M
26. Segment(C, M) → p
27. Line(C, M) → q
28. OrthogonalLine(A, q) → r
29. Intersect(q, r) → N
30. Line(C, B) → s
31. OrthogonalLine(A, s) → c
32. Intersect(s, c) → O
33. Line(N, O) → e
34. OrthogonalLine(C, e) → i_1
35. Intersect(e, i_1) → P
36. Angle(A, C, M) → θ
37. Angle(O, C, P) → ι
38. Segment(C, P) → j_1
39. Min({h, p, i, j_1}) → v
40. Circle(C, (0.4 * v)) → c_1
41. Intersect(c_1, h) → Q,
42. Intersect(c_1, p) → R,
43. CircleSector(C, Q, R) → d_1
44. Dilate(C, If[0 < o ≤ 1, 1 - o, 0], M) → C'_2
45. Segment(C, C'_2) → t
46. Angle(M, N, A) → κ_1
47. Dilate(M, If[1 < o ≤ 2, 2 - o, 0], N) → M'
48. Dilate(A, If[1 < o ≤ 2, 2 - o, 0], N) → A'_1
49. Segment(M, M') → f_1
50. Segment(A, A'_1) → k_1
51. Dilate(A, If[2 < o ≤ 3, 3 - o, 0], O) → A'_2
52. Segment(A, A'_2) → l_1
53. Dilate(N, If[3 < o ≤ 4, 4 - o, 0], O) → N'
54. Segment(N, N') → m_1
55. Dilate(O, If[4 < o ≤ 5, 5 - o, 0], P) → O'
56. Dilate(C, If[4 < o ≤ 5, 5 - o, 0], P) → C'_3
57. Angle(C, P, O) → ζ
58. Segment(O, O') → n_1
59. Segment(C, C'_3) → p_1
60. Rotate(Q, If[5 < o ≤ 6, ((o - 5) * θ), θ], C) → Q'
61. CircleSector(C, Q, Q') → e_1
62. Angle(A, C, B) → κ
63. Polygon(A, B, C) → poly1, c_2, a_1, b
64. Rotate(d_1, If[6.5 < o ≤ 7.5, ((o - 6.5) * κ), κ], C) → q_1
65. Circle(B, 1) → d
66. Circle(C, 1) → t_1
67. Intersect(d, s) → D, F
68. Intersect(t_1, s) → G, H
69. Ray(B, F) → l
70. Ray(C, G) → b_1
71. Angle(C, O, A) → β