直角三角形与外接圆的几何构造与性质探究

GeoGebra 命令及参数

1. Center(c) → A
2. Rotate(B, pi / 3, A) → B'_1
3. Intersect(h, i) → C
4. Midpoint(A, B'_1) → J
5. Angle(B, A, B'_1) → β
6. Rotate(B, pi / 4, A) → B'_2
7. Angle(B, A, B'_2) → γ
8. Intersect(g, i) → D
9. Polygon(A, D, B'_2) → poly2, b'_2, a_2, d
10. Polygon(A, C, B'_1) → poly3, b'_1, a_3, c_1
11. Dilate(A, If[0 < a ≤ 1, 1 - a, 0], J) → A'_1
12. Segment(A, A'_1) → k
13. Dilate(J, If[1 < a ≤ 2, 2 - a, 0], B'_1) → F'
14. CircleArc(A, B'_1, B) → p
15. Textfield(r) → InputBox1
16. Segment(J, F') → m
17. Midpoint(C, B'_1) → K
18. Dilate(C, If[0 < a ≤ 1, 1 - a, 0], K) → C'
19. Dilate(K, If[1 < a ≤ 2, 2 - a, 0], B'_1) → K'
20. Segment(C, C') → j
21. Segment(K, K') → l
22. Angle(B'_1, C, A) → α
23. Dilate(A, If[2 < a ≤ 3, 3 - a, 0], C) → A'
24. Segment(A, A') → n
25. Rotate(A, If[3.5 < a ≤ 4.5, ((a - 3.5) * pi / 3), pi / 3], A) → A'_3
26. Rotate(A', If[3.5 < a ≤ 4.5, ((a - 3.5) * pi / 3), pi / 3], A) → A''
27. Segment(A'_3, A'') → n'
28. Rotate(A'_3, If[4.5 < a ≤ 5.5, ((a - 4.5) * pi), pi], J) → F
29. Rotate(A'', If[4.5 < a ≤ 5.5, ((a - 4.5) * pi), pi], J) → A'''
30. Segment(F, A''') → n''
31. CircleArc(A, B, B'_1) → q
32. RotateText(text4, ((-pi)) / 2) → text6
33. Mirror(A, j) → A'_{2}
34. Mirror(C, j) → C'_{1}
35. Mirror(B'_1, j) → E
36. Polygon(A'_{2}, C'_{1}, E) → poly3', e, a'_{2}, c'_{1}
37. Mirror((0, 0), A') → G
38. Rotate((0, 0), (-(pi / 3)), G) → H
39. Mirror(F, l) → F'_{1}
40. Mirror(A''', l) → I
41. Segment(F'_{1}, I) → n'''
42. Mirror(A'_3, j) → L
43. Mirror(A'', j) → A'''_{1}
44. Segment(L, A'''_{1}) → n''_{1}
45. Mirror(A, j) → A'_{4}
46. Mirror(A', j) → A''_{1}
47. Segment(A'_{4}, A''_{1}) → n'_{1}
48. Angle(N, M, (0, 0)) → δ