动态几何作图范例：三角形重心与垂心关系

GeoGebra 命令及参数

1. Circle(A, B) → c
2. Distance(A, B) → a
3. PointIn(b) → C_1
4. Semicircle(A, C_1) → d
5. Semicircle(C_1, A) → e
6. Intersect(c, d, 1) → D_1
7. Intersect(c, e, 1) → C
8. Line(C_1, C) → f
9. Line(C_1, D_1) → g
10. Line(C, g) → h
11. Intersect(c, h) → F, D
12. Line(C_1, D) → i
13. Intersect(c, i, 2) → E
14. Line(C, E) → j
15. Intersect(g, j) → G
16. Angle(A, D_1, G) → α
17. Angle(C_1, C, A) → β
18. Dilate(C_1, If[0 < k ≤ 1, 1 - k, 0], G) → H
19. Midpoint(C, C_1) → I
20. Dilate(C_1, If[0 < k ≤ 1, 1 - k, 0], I) → J
21. Segment(C_1, J) → l
22. Segment(C_1, H) → m
23. Dilate(G, If[0 < k ≤ 1, 1 - k, 0], G) → G'
24. Dilate(A, If[1 < k ≤ 2, 2 - k, 0], D_1) → A'
25. Dilate(A, If[1 < k ≤ 2, 2 - k, 0], C) → A'_1
26. Segment(A, A') → n
27. Segment(A, A'_1) → p
28. Dilate(G, If[1 < k ≤ 2, 2 - k, 0], D_1) → G'_1
29. Dilate(I, If[1 < k ≤ 2, 2 - k, 0], C) → I'
30. Segment(G, G'_1) → q
31. Segment(I, I') → r
32. Rotate(A, 90°, C) → A'_2
33. Angle(A, C, A'_2) → γ
34. Ray(C, A'_2) → s
35. Circle(C_1, (0.4 * Distance[C_1, G])) → t
36. Angle(G, C_1, C) → δ
37. Intersect(i, h) → K
38. Dilate(C, If[3 < k ≤ 4, 4 - k, 0], K) → C'
39. Segment(C, C') → f_1
40. Intersect(t, m) → L,
41. Rotate(L, If[4 < k ≤ 5, ((k - 4) * δ), δ], C_1) → L'
42. CircleSector(C_1, L, L') → c_1
43. Dilate(C_1, If[5.5 < k ≤ 6.5, 6.5 - k, 0], C) → M
44. Vector(C_1, M) → u
45. Translate(c_1, u) → d_1
46. Dilate(K, If[6 < k ≤ 7, 7 - k, 0], E) → K'
47. Segment(K, K') → g_1
48. Dilate(E, If[7 < k ≤ 8, 8 - k, 0], C_1) → E'
49. Segment(E, E') → h_1
50. Dilate(C, If[8.5 < k ≤ 9.5, 9.5 - k, 0], E) → C'_1
51. Segment(C, C'_1) → i_1
52. Dilate(E, If[9.5 < k ≤ 10.5, 10.5 - k, 0], G) → E'_1
53. Segment(E, E'_1) → j_1
54. Segment(C_1, G) → k_1
55. Segment(G, D_1) → l_1
56. Rotate(C_1, If[11.5 < k ≤ 12.5, ((-(k - 11.5)) * π), (-π)], G) → N
57. Rotate(G, If[11.5 < k ≤ 12.5, ((-(k - 11.5)) * π), (-π)], G) → G'_2
58. Segment(N, G'_2) → m_1