贝特朗悖论第二种方法：随机弦与等边三角形内切圆

GeoGebra 命令及参数

1. Circle(O, 3) → c
2. Point(c) → A
3. Tangent(A, c) → tangentLine,
4. Point(tangentLine) → B_1
5. Rotate(B_1, α, A) → B'
6. Angle(B_1, A, B') → β
7. Rotate(B_1, 60°, A) → B'_1
8. Angle(B_1, A, B'_1) → γ
9. Line(A, B'_1) → e
10. Intersect(c, e, 2) → D
11. Polygon(A, D, 3) → poly1, f, g, h, E
12. Line(A, B') → line_{AB}
13. Intersect(c, line_{AB}, 2) → B
14. Segment(A, B) → seg_{AB}
15. Line(A, O) → diamLine
16. Intersect(c, diamLine, 2) → C
17. Segment(A, C) → diam
18. Circle(A, (m * diam)) → MConic
19. Intersect(MConic, diam, 1) → M_{PQ}
20. OrthogonalLine(M_{PQ}, diam) → perpToDiamLine
21. Intersect(c, perpToDiamLine, 2) → Q
22. Intersect(c, perpToDiamLine, 1) → P
23. Segment(P, Q) → seg_{PQ}
24. Rotate(A, 30°, C) → A'
25. Angle(A, C, A') → δ
26. Line(C, A') → i
27. Intersect(c, i, 2) → F
28. Polygon(F, C, 3) → poly2, j, k, l, G
29. Circle(O, (0.25 * diam)) → d
30. Segment(M_{ST}, O) → seg_{OMST}
31. OrthogonalLine(M_{ST}, seg_{OMST}) → line_{ST}
32. Intersect(c, line_{ST}, 1) → S
33. Intersect(c, line_{ST}, 2) → T
34. Segment(S, T) → seg_{ST}