维瓦尼亚定理

GeoGebra 命令及参数

1. Polygon(B, C, 3) → poly1, a, b, c, A
2. PointIn(poly1) → M
3. OrthogonalLine(M, b) → d
4. OrthogonalLine(M, a) → e
5. OrthogonalLine(M, c) → f
6. Intersect(d, b) → P
7. Intersect(e, a) → N
8. Intersect(f, c) → Q
9. Segment(M, P) → g
10. Segment(M, Q) → h
11. Segment(M, N) → i
12. Segment(A, Q) → j
13. Segment(B, N) → k
14. Segment(C, P) → l
15. Angle(M, Q, A) → α
16. Angle(M, P, C) → β
17. Angle(M, N, B) → γ
18. Segment(A, M) → p
19. Segment(B, M) → q
20. Segment(M, C) → r
21. Rotate(P, 30*°, M) → P'
22. Angle(P, M, P') → δ
23. Ray(M, P') → s
24. Intersect(b, s) → D
25. Intersect(i, poly1) → E
26. Polygon(D, M, 3) → poly2, t, a_1, b_1, F
27. Segment(M, F) → c_1
28. Segment(M, D) → d_1
29. OrthogonalLine(D, a_1) → e_1
30. Intersect(a_1, c_1) → G
31. Intersect(a_1, c_1) → H
32. Intersect(e_1, a_1) → I
33. Segment(D, I) → f_1
34. Rotate(N, 30*°, M) → N'
35. Angle(N, M, N') → ε
36. Ray(M, N') → g_1
37. Intersect(a, g_1) → J
38. Polygon(J, M, 3) → poly3, h_1, i_1, j_1, K
39. Line(M, a) → k_1
40. Intersect(c, k_1) → L
41. Polygon(L, M, 3) → poly4, l_1, m_1, n_1, O
42. OrthogonalLine(O, k_1) → p_1
43. Intersect(k_1, p_1) → R
44. Segment(O, R) → q_1
45. Segment(M, K) → r_1
46. Segment(M, J) → s_1
47. Segment(D, A) → t_1
48. Point(t_1) → S
49. Vector(D, S) → u
50. Translate(poly2, u) → poly2'
51. Translate(D, u) → D'
52. Translate(I, u) → I'
53. Segment(D', I') → a_2
54. Translate(M, u) → M'
55. Translate(F, u) → F'
56. Segment(M', F') → b_2