维瓦尼定理：等边三角形内一点到三边垂线段之和等于高

GeoGebra 命令及参数

1. Ray(A, B) → baseRay
2. Point(baseRay) → C
3. Polygon(A, C, 3) → poly1, l_3, l_1, l_2, D
4. PointIn(poly1) → P
5. OrthogonalLine(P, l_2) → p_1
6. OrthogonalLine(P, l_1) → p_2
7. OrthogonalLine(P, l_3) → p_3
8. Intersect(p_1, l_2) → F
9. Intersect(p_3, baseRay) → G
10. Intersect(p_2, l_1) → H
11. Segment(F, P) → h_4
12. Segment(H, P) → h_5
13. Segment(G, P) → h_3
14. Line(P, l_3) → horizon
15. Intersect(horizon, l_2) → I
16. Intersect(horizon, l_1) → J
17. Polygon(I, P, 3) → poly2, e_3, e_2, e_1, K
18. Polygon(P, J, 3) → poly3, f_3, f_1, f_2, L
19. OrthogonalLine(K, e_3) → p_4
20. OrthogonalLine(L, f_3) → p_5
21. Intersect(p_4, h_4) → M
22. Intersect(p_5, h_5) → N
23. If(k ≤ 1, k, 1) → k_1
24. If(k ≥ 1, If[k ≥ 2, 1, k - 1], 0) → k_2
25. Rotate(poly2, ((k_1 * 120))°, M) → poly2'
26. Rotate(poly3, (((-k_2) * 120))°, N) → poly3'
27. Rotate(F, ((k_1 * 120))°, M) → F'
28. Rotate(P, ((k_1 * 120))°, M) → P_r1
29. Segment(F', P_r1) → h_2
30. Rotate(H, (((-k_2) * 120))°, N) → H'
31. Rotate(P, (((-k_2) * 120))°, N) → P_r2
32. Segment(H', P_r2) → h_7
33. If(k ≥ 2, k - 2, 0) → k_3
34. Translate(poly3', Vector[(k_3 * Vector[L, D])]) → poly3''
35. Translate(H', Vector[(k_3 * Vector[L, D])]) → H''
36. Translate(P_r2, Vector[(k_3 * Vector[L, D])]) → P_t
37. Segment(H'', P_t) → h_1
38. Angle(P, G, A) → α
39. Angle(P, F, D) → β
40. Angle(P, H, C) → γ