两切线所成角的探索

GeoGebra 命令及参数

1. Circle(A, B) → c
2. Tangent(C, c) → a, b
3. Intersect(c, a) → D
4. Intersect(c, b) → E
5. Ray(C, D) → d
6. Ray(C, E) → e
7. CircleArc(A, D, E) → f
8. CircleArc(A, E, D) → g
9. Point(f) → F
10. Point(g) → G
11. Segment(F, D) → h
12. Segment(F, E) → i
13. Segment(G, D) → j
14. Segment(G, E) → k
15. Circle(F, 1.5) → p
16. Circle(G, 1.5) → q
17. Intersect(p, h, 1) → H
18. Intersect(p, i, 1) → I
19. Intersect(q, j, 1) → J
20. Intersect(q, k, 1) → K
21. CircleSector(F, I, H) → r
22. CircleSector(G, J, K) → s
23. Segment(A, E) → l
24. Angle(C, E, A) → α
25. Angle(A, D, C) → β
26. Segment(A, D) → m
27. Vector(F, G) → u
28. Segment(F, G) → t
29. Intersect(p, t) → L,
30. Translate(r, u) → r'
31. Line(F, k) → a_1
32. Intersect(p, a_1) → M, N
33. Angle(H, F, N) → γ
34. Rotate(r', γ, G) → r''
35. Dilate(F, If[0 < n < 1, 1 - n, 0], G) → F'
36. Vector(F, F') → v
37. Translate(r, v) → r'_1
38. Rotate(r'_1, If[0 < n < 1, (n * γ), 0], F') → c_1
39. Angle(I, F, H) → δ
40. Rotate(K, (-δ), G) → K'
41. Angle(K', G, K) → ε
42. CircleSector(G, J, K') → d_1
43. Vector(G, C) → w
44. Line(G, d) → b_1
45. Translate(d_1, w) → e_1
46. Dilate(G, If[1.5 < n < 2.5, 2.5 - n, 0], C) → G'
47. Vector(G, G') → u_1
48. Translate(d_1, u_1) → f_1
49. Translate(K', u_1) → K''
50. Point(e) → O
51. Line(G, e) → g_1
52. Intersect(q, g_1) → P, Q
53. Angle(K', G, Q) → ζ
54. Rotate(e_1, ζ, C) → h_1
55. Rotate(f_1, If[1.5 < n < 2.5, ((n - 1.5) * ζ), 0], G') → k_1
56. Angle(E, F, D) → η
57. Angle(D, G, E) → θ