圆周角定理推论一：直径所对圆周角为直角

GeoGebra 命令及参数

1. Circle(A, B) → c
2. Point(c) → C
3. Point(c) → D
4. CircleArc(A, D, C) → d
5. Point(d) → E
6. Point(d) → F
7. CircleArc(A, C, D) → e
8. Segment(A, C) → a
9. Segment(A, D) → b
10. Segment(E, C) → f
11. Segment(E, D) → g
12. Segment(F, C) → h
13. Segment(F, D) → i
14. Angle(C, A, D) → α
15. Rotate(C, α / 2, A) → C'
16. Angle(C, A, C') → β
17. Segment(A, C') → j
18. Circle(E, (0.35 * Distance[A, B])) → k
19. Intersect(k, f, 1) → G
20. Intersect(k, g, 1) → H
21. Circle(F, (0.35 * Distance[A, B])) → p
22. Intersect(p, h, 1) → J
23. Intersect(p, i, 1) → K
24. CircleSector(E, G, H) → q
25. CircleSector(F, J, K) → r
26. Dilate(E, If[0 < l ≤ 1, 1 - l, 0], A) → E'
27. Vector(E, E') → u
28. Line(E, a) → m
29. Intersect(k, m, 2) → L
30. Angle(L, E, G) → γ
31. Dilate(E, If[2 < l ≤ 3, 3 - l, 0], A) → E'_1
32. Vector(E, E'_1) → v
33. Line(E, j) → n
34. Intersect(k, n, 2) → M
35. Angle(M, E, G) → δ
36. Circle(A, (0.35 * Distance[A, B])) → t
37. Intersect(t, a, 1) → N
38. Intersect(t, j, 1) → O
39. Intersect(t, c, 1) → I
40. Intersect(t, b) → P,
41. CircleArc(A, N, P) → c_1
42. Point(d) → Q
43. Segment(Q, C) → a_1
44. Segment(Q, D) → b_1
45. Dilate(E, If[0 < l ≤ 1, 1 - l, 0], F) → E'_2
46. Dilate(E, If[0 < l ≤ 1, 1 - l, 0], Q) → E'_3
47. Vector(E, E'_2) → w
48. Vector(E, E'_3) → s
49. Translate(q, s) → q'_1
50. Line(E, i) → d_1
51. Intersect(k, d_1) → R, S
52. Angle(H, E, S) → ε
53. Line(E, a_1) → e_1
54. Intersect(k, e_1) → T, U
55. Angle(U, E, G) → ζ
56. CircleArc(A, D, C) → g_1
57. Rotate(q'_1, If[0 < l ≤ 1, ((-l) * ζ), (-ζ)], E'_3) → f_1
58. Dilate(Q, If[2 < l ≤ 3, 3 - l, 0], F) → Q'
59. Vector(Q, Q') → u_1
60. Translate(f_1, u_1) → h_1
61. Line(Q, h) → i_1
62. Point(i_1) → V
63. Angle(V, Q, C) → θ
64. Rotate(h_1, If[2 < l ≤ 3, ((-(l - 2)) * θ), (-θ)], Q') → k_1