平面几何基础证明示例6（分步引导）

GeoGebra 命令及参数

1. Circle(O, 4) → c
2. Point(c) → B
3. Point(c) → X
4. Segment(X, B) → g
5. Tangent(X, c) → b,
6. Point(b) → Y
7. Segment(X, Y) → f
8. AngularBisector(f, g) → h, i
9. Intersect(c, h) → A', A
10. Polygon((x(X) + 0.15, y(X) + 0.05), (x(X) - 0.15, y(X) - 0.02), (x(A) - 0.1, y(A) - 0.05), (x(A) + 0.1, y(A))) → RectAX, e_1, f_1, i_1, j_1
11. Polygon((x(A) + 0.1, y(A) + 0.05), (x(A) - 0.1, y(A)), (x(B) - 0.1, y(B)), (x(B) + 0.1, y(B))) → RectAB, t, a_1, c_1, d_1
12. Midpoint(I, J) → K'
13. Point(c) → C
14. Segment(C, X) → d
15. Point(d) → E
16. Segment(B, E) → e
17. Segment(E, Y) → a
18. Intersect(a, g) → D
19. Angle(h, f) → α
20. Angle(g, h) → β
21. Segment(X, A) → j
22. Segment(B, A) → k
23. Intersect(c, a) → F, A_1
24. Distance(A, B) → distanceAB
25. Distance(A, X) → distanceAX
26. Point(g) → G
27. Point(k) → H
28. Polygon(G, B, H) → poly1, h_1, g_1, b_1
29. Polygon(L, M, N, P, Q, R, S) → poly2, l, m, n, p, q, r, s
30. Angle(A, B, X) → γ
31. IsInRegion(K, poly1) → show1
32. If(IsInRegion[K, RectAX] ∨ IsInRegion[K, RectAB], true, false) → show2
33. Point(d) → T
34. Point(a) → U
35. Polygon(T, C, U) → poly3, u, t_1, c_2
36. IsInRegion(K, poly3) → show3
37. Point(e) → Z
38. Polygon(U, C, Z) → poly4, k_1, l_1, m_1
39. IsInRegion(K, poly4) → show4
40. Angle(B, E, Y) → ε
41. Point(a) → V
42. Point(k) → W
43. Polygon(V, A, W) → poly5, w, v, a_2
44. Point(d) → B_1
45. Point(g) → C_1
46. Polygon(B_1, X, C_1) → poly6, c_3, b_2, d_2
47. If(IsInRegion[K, poly5] ∨ IsInRegion[K, poly6], true, false) → show5
48. Angle(C, X, B) → ζ
49. Angle(D, A, B) → η
50. Angle(A, C, X) → δ
51. Polygon(C, D, X) → poly7, e_2, c_4, d_3
52. IsInRegion(K, poly7) → show7
53. Polygon(C, B, A) → poly8, a_3, c_5, b_3
54. IsInRegion(K, poly8) → show8