泰勒斯定理（版本A）——交互式探究与问题引导

GeoGebra 命令及参数

1. Circle(A, B) → c
2. Point(c) → C
3. Line(C, A) → a
4. Intersect(c, a, 2) → D
5. CircleArc(A, C, D) → d
6. CircleArc(A, D, C) → e
7. Point(e) → E
8. Segment(C, D) → h
9. Dilate(C, If[0 < b ≤ 1, 1 - b, 0], A) → C'
10. Segment(C, C') → i
11. Dilate(A, If[1 < b ≤ 2, 2 - b, 0], D) → A'
12. Segment(A, A') → j
13. Rotate(C, If[2 < b ≤ 3, ((-(b - 2)) * π), (-π)], A) → C'_1
14. Rotate(C', If[2 < b ≤ 3, ((-(b - 2)) * π), (-π)], A) → C''
15. Segment(C'_1, C'') → i'
16. Rotate(C, If[3 < b ≤ 4, ((b - 3) * π), π], A) → C'_2
17. CircleArc(A, C, C'_2) → k
18. Dilate(D, If[5 < b ≤ 6, 6 - b, 0], E) → D'
19. Segment(D, D') → f
20. Ray(D, E) → g
21. Point(g) → F
22. Ray(E, F) → l
23. Dilate(C, If[5 < b ≤ 6, 6 - b, 0], E) → C'_3
24. Segment(C, C'_3) → m
25. Min({m, f}) → n
26. Circle(E, (0.2 * n)) → p
27. Intersect(p, l) → G,
28. Intersect(c, m, 1) → H
29. Intersect(p, m) → I,
30. CircleSector(E, G, I) → q
31. Rotate(q, If[6.5 < b ≤ 7.5, ((b - 6.5) * π / 2), π / 2], E) → q'