圆内接角定理证明练习（案例2）

GeoGebra 命令及参数

1. Circle(O, B_1) → c
2. Point(c) → A
3. Line(A, O) → f
4. Intersect(c, f, 2) → D_1
5. CircleArc(O, D_1, A) → d
6. CircleArc(O, A, D_1) → e
7. Point(e) → B
8. Point(d) → C
9. Segment(A, B) → g
10. Segment(A, C) → h
11. Circle(A, (0.25 * Distance[O, B_1])) → k
12. Intersect(k, g, 1) → G
13. Intersect(k, h, 1) → H
14. CircleSector(A, G, H) → p
15. Dilate(A, If[0 < a ≤ 1, 1 - a, 0], O) → C'
16. Segment(A, C') → i
17. Dilate(O, If[1 < a ≤ 2, 2 - a, 0], D_1) → A'
18. Segment(O, A') → j
19. Dilate(O, If[3 < a ≤ 4, 4 - a, 0], B) → A'_1
20. Segment(O, A'_1) → l
21. Angle(A, O, B) → α
22. Angle(C, O, A) → β
23. Rotate(O, If[4 < a ≤ 5, ((-(a - 4)) * α), (-α)], O) → A'_2
24. Rotate(A'_1, If[4 < a ≤ 5, ((-(a - 4)) * α), (-α)], O) → I
25. Segment(A'_2, I) → l'
26. Rotate(O, If[5 < a ≤ 6, ((-(a - 5)) * β), (-β)], O) → A'_3
27. Rotate(A'_2, If[5 < a ≤ 6, ((-(a - 5)) * β), (-β)], O) → J
28. Rotate(I, If[5 < a ≤ 6, ((-(a - 5)) * β), (-β)], O) → I'
29. Segment(J, I') → l''
30. Circle(B, (0.25 * Min[g, l])) → q
31. Intersect(q, g) → K,
32. Intersect(q, l) → L,
33. CircleSector(B, L, K) → r
34. Angle(O, B, A) → γ
35. Rotate(K, If[6 < a ≤ 7, ((-(a - 6)) * γ), (-γ)], B) → K'
36. CircleSector(B, K', K) → s
37. Polygon(B, O, A) → poly1, c_1, e_1, a_1
38. Polygon(O, C, A) → poly2, c_2, a_2, f_1
39. Dilate(A, If[0 < m ≤ 1, 1 - m, 0], O) → C'_1
40. Vector(A, C'_1) → u
41. Translate(p, u) → p'
42. Line(O, g) → n
43. Line(O, h) → t
44. Intersect(d, t) → M, E
45. Angle(M, O, C) → δ
46. Rotate(p', If[1 < m ≤ 2, ((m - 1) * δ), δ], O) → p''
47. Intersect(e, n) → N, D
48. Angle(B, O, N) → ε
49. Dilate(A, If[2 < m ≤ 3, 3 - m, 0], O) → C'_2
50. Vector(A, C'_2) → v
51. Translate(p, v) → p'_1
52. Circle(O, Radius[k]) → g_1
53. Rotate(n, δ, O) → n'
54. Rotate(p'_1, If[2 < m ≤ 3, ((-(m - 2)) * ε), (-ε)], C'_2) → d_1
55. CircleArc(O, B, C) → h_1
56. CircleArc(O, C, B) → k_1