导数与相似三角形动画演示：切线斜率与几何关系可视化

GeoGebra 命令及参数

1. Line(A, B) → g
2. Slope(g) → m
3. Root(s_1, x(A), x(B)) → N
4. Intersect(n, h, 1) → C
5. Intersect(i, j) → D
6. Tangent(D, f) → k
7. Intersect(k, t) → K
8. Intersect(f, k, (0, 0)) → E
9. Circle(A, d) → e_1
10. Intersect(e_1, l, 2) → F
11. Intersect(g, p) → G
12. Intersect(g, q) → H
13. Intersect(g, r) → I
14. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], B) → A'
15. Segment(A, A') → f_1
16. Intersect(k, s) → J
17. Dilate(G, If[1 < o ≤ 2, 2 - o, 0], F) → G'
18. Segment(G, G') → g_1
19. Dilate(F, If[2 < o ≤ 3, 3 - o, 0], A) → F'
20. Segment(F, F') → h_1
21. Polygon(A, G, F) → poly1, f_2, a_1, g_2
22. Angle(G, F, A) → α
23. Dilate(O, If[4 < o ≤ 5, 5 - o, 0], J) → E'
24. Dilate(O, If[4 < o ≤ 5, 5 - o, 0], K) → E'_1
25. Segment(E, E'_1) → i_1
26. Segment(E, E') → j_1
27. Intersect(k, q) → L
28. Intersect(k, r) → M
29. Ray(K, M) → k_1
30. Ray(J, L) → l_1
31. Ray(B, I) → m_1
32. Ray(A, H) → n_1
33. Dilate(A, If[5 < o ≤ 6, 6 - o, 0], E) → A'_1
34. Vector(A, A'_1) → u
35. Translate(A, u) → A'_2
36. Translate(G, u) → G'_1
37. Translate(F, u) → F'_1
38. Polygon(A'_2, G'_1, F'_1) → poly1', f'_1, a'_2, g'_1
39. Translate(F, u) → F'_2
40. Translate(F', u) → F''
41. Segment(F'_2, F'') → p_1
42. Translate(G, u) → G'_2
43. Translate(G', u) → G''
44. Segment(G'_2, G'') → q_1
45. Angle(G'_2, F'_2, A'_2) → β
46. Segment(A'_2, G'_2) → r_1
47. Textfield(f) → InputBox1