直角三角形与正方形组合的几何构造

GeoGebra 命令及参数

1. Segment(A, B) → f
2. OrthogonalLine(A, f) → g
3. Point(g) → C
4. Segment(C, B) → h
5. Midpoint(h) → D
6. Polygon(C, D, 4) → poly1, i, j, k, l, E, F
7. Polygon(D, B, 4) → poly2, m, n, p, q, G, H
8. Ray(A, H) → r
9. Polygon(B, C, A) → t1, a, b, c
10. Segment(C, F) → t
11. Segment(F, H) → d
12. Segment(H, D) → e
13. Segment(H, G) → f_1
14. Segment(G, B) → g_1
15. Segment(C, D) → s
16. Segment(D, B) → h_1
17. Angle(C, F, H) → β
18. Angle(F, H, D) → γ
19. Angle(H, D, C) → δ
20. Angle(H, G, B) → ε
21. Dilate(A, If[4 < o ≤ 5, 5 - o, 0], H) → A'
22. Segment(A, A') → i_1
23. Segment(A, C) → j_1
24. Dilate(B, If[0 < o ≤ 1, 1 - o, 0], H) → B'
25. Segment(B, B') → k_1
26. Circle(H, (0.4 * Min[{j_1, e, f}])) → c_1
27. Intersect(c_1, e, 1) → I
28. Intersect(c_1, f_1, 1) → J
29. Rotate(J, If[1 < o ≤ 2, ((-(o - 1)) * π / 4), ((-π)) / 4], H) → J'
30. CircleSector(H, J', J) → d_1
31. Rotate(d_1, If[3 < o ≤ 4, ((-(o - 3)) * π / 4), ((-π)) / 4], H) → e_1
32. Semicircle(A, H) → p_1
33. Midpoint(i_1) → K
34. Rotate(H, If[6 < o ≤ 7, ((o - 6) * π), π], K) → H'
35. Vector(H, H') → u
36. Translate(e_1, u) → q_1
37. Line(A, k_1) → l_1
38. Point(l_1) → L
39. Angle(L, A, H) → α
40. Rotate(q_1, If[6 < o ≤ 7, ((o - 6) * α), α], H') → r_1
41. Angle(B, A, C) → ζ