圆周角定理（无字证明）

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, (0.25 * Distance[A, B])) → k
19. Intersect(k, f, 1) → G
20. Intersect(k, g, 1) → H
21. Circle(F, (0.25 * 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. Translate(q, u) → q'
29. Line(E, a) → m
30. Intersect(k, m, 2) → L
31. Angle(L, E, G) → γ
32. Rotate(q', If[1 < l ≤ 2, ((-(l - 1)) * γ), (-γ)], A) → q''
33. Dilate(E, If[2 < l ≤ 3, 3 - l, 0], A) → E'_1
34. Vector(E, E'_1) → v
35. Translate(q, v) → q'_1
36. Line(E, j) → n
37. Intersect(k, n, 2) → M
38. Angle(M, E, G) → δ
39. Rotate(q'_1, If[3 < l ≤ 4, ((l - 3) * (360° - δ)), (-δ)], A) → s
40. Circle(A, (0.25 * Distance[A, B])) → t
41. Intersect(t, a, 1) → N
42. Intersect(t, j, 1) → O
43. Intersect(t, c, 1) → I
44. Intersect(t, b) → P,
45. CircleArc(A, N, P) → c_1