直角三角形高与斜边：几何平均的相似三角形验证

GeoGebra 命令及参数

1. Semicircle(A, B) → d
2. Point(d) → C
3. Segment(C, B) → f
4. Segment(A, C) → e
5. Segment(A, B) → a
6. Min(a, f) → m
7. Min(a, e) → l
8. Min(l, m) → n
9. Midpoint(a) → C_1
10. OrthogonalLine(C_1, a) → b
11. Circle(C_1, A) → c
12. OrthogonalLine(C, a) → g
13. Intersect(g, a) → E
14. Segment(C, E) → h
15. Angle(B, E, C) → α
16. Angle(A, C, B) → β
17. Polygon(A, E, C) → poly1, d_1, a_1, e_1
18. Polygon(E, B, C) → poly2, d_2, e_2, b_1
19. Circle(A, (0.2 * n)) → k
20. Circle(C, (0.2 * n)) → p
21. Circle(B, (0.2 * n)) → q
22. Intersect(p, e_1, 1) → F
23. Intersect(a_1, b_1) → G
24. Intersect(a_1, b_1) → H
25. Intersect(p, h, 1) → I
26. Intersect(p, f, 1) → J
27. Intersect(q, a, 1) → K
28. Intersect(q, f, 1) → L
29. Intersect(k, a, 1) → M
30. Intersect(k, e, 1) → N
31. CircleSector(A, M, N) → r
32. Dilate(C, If[-2 < i < -1, -1 - i, 0], E) → D'
33. Segment(C, D') → j
34. CircleSector(B, L, K) → t
35. Angle(C, E, A) → γ
36. Dilate(A, If[-0.5 < i ≤ 0.5, 0.5 - i, 0], C) → A'
37. Vector(A, A') → u
38. Translate(r, u) → r'
39. CircleArc(A, M, N) → f_1
40. Dilate(B, If[1.5 < i ≤ 2.5, 2.5 - i, 0], C) → B'
41. Vector(B, B') → v
42. Translate(t, v) → t'
43. CircleArc(B, L, K) → g_1
44. Polygon(A, B, C) → poly3, d_3, a_2, b_2
45. Rotate(r', If[0.5 < i ≤ 1.5, ((-(i - 0.5)) * π / 2), -1.5707963267948966], C) → r''
46. Translate(t, v) → t'_1
47. Rotate(t'_1, If[2.5 < i ≤ 3.5, ((i - 2.5) * 90°), 90°], C) → s
48. Intersect(a, j) → D