Archimedes双圆构造：几何作图与圆的性质

GeoGebra 命令及参数

1. Midpoint(A, B) → C
2. Segment(C, A) → g
3. Circle(C, B) → c
4. Segment(A, B) → a
5. Point(g) → D
6. Midpoint(D, A) → G
7. Midpoint(D, B) → H
8. Circle(G, D) → d
9. Circle(H, D) → e
10. OrthogonalLine(D, a) → b
11. Intersect(c, b, 2) → E
12. Intersect(c, b, 1) → F
13. Segment(E, F) → f
14. Distance(G, A) → r
15. Distance(H, B) → R
16. Segment(I, G) → j
17. OrthogonalLine(I, f) → k
18. Intersect(b, k) → J
19. Segment(I, J) → l
20. Intersect(d, j) → K,
21. Segment(I, K) → m
22. Circle(D, G) → p
23. Intersect(p, a, 2) → L
24. OrthogonalLine(L, a) → i
25. Parabola(G, i) → q
26. Circle(D, H) → s
27. Line(A, B) → n
28. Intersect(s, n, 1) → M
29. OrthogonalLine(M, n) → t
30. Parabola(H, t) → c_1
31. Ray(C, I) → a_1
32. Intersect(c, a_1, 1) → N
33. Segment(I, N) → b_1
34. Circle(G, C) → d_1
35. Intersect(d_1, n, 1) → O
36. OrthogonalLine(O, n) → e_1
37. Parabola(C, e_1) → f_1
38. Circle(H, C) → g_1
39. Intersect(g_1, n, 2) → P
40. OrthogonalLine(P, n) → h_1
41. Parabola(C, h_1) → k_1
42. Intersect(c_1, k_1, 2) → Q
43. Intersect(c_1, k_1, 1) → S
44. Intersect(q, f_1, 1) → T
45. Intersect(q, f_1, 2) → U
46. OrthogonalLine(Q, f) → i_1
47. OrthogonalLine(S, f) → j_1
48. OrthogonalLine(U, f) → l_1
49. OrthogonalLine(T, f) → m_1
50. Intersect(i_1, f) → V
51. Intersect(m_1, f) → W
52. Intersect(l_1, f) → Z
53. Intersect(j_1, f) → A_1
54. Circle(Q, V) → p_1
55. Circle(T, W) → q_1
56. Circle(U, Z) → r_1
57. Circle(S, A_1) → s_1
58. Area(p_1) → o
59. PointIn(p_1) → Pointp1
60. Area(q_1) → u
61. PointIn(q_1) → Pointq1