三角形的特征点：中点、角平分与垂线构造

GeoGebra 命令及参数

1. Polygon(A, B, C) → t1, c, a, b
2. Midpoint(A, B) → D
3. Midpoint(B, C) → E
4. Midpoint(C, A) → F
5. OrthogonalLine(D, c) → f
6. OrthogonalLine(F, b) → g
7. OrthogonalLine(E, a) → h
8. AngularBisector(c, a) → k, l
9. AngularBisector(b, a) → m, n
10. AngularBisector(c, b) → i, j
11. Line(A, E) → p
12. Line(B, F) → q
13. Line(D, C) → r
14. Intersect(q, p) → G
15. Intersect(n, j) → H_{1}
16. Intersect(h, f) → O
17. OrthogonalLine(A, a) → s
18. OrthogonalLine(B, b) → t
19. OrthogonalLine(C, c) → d
20. Intersect(s, d) → H
21. Line(H, O) → e
22. Angle(C, E, O) → α
23. Angle(O, F, C) → β
24. Angle(B, D, O) → γ
25. Angle(c, d) → δ
26. Angle(b, t) → ε
27. Angle(a, s) → ζ
28. Circle(O, A) → c_1
29. Segment(A, D) → f_1
30. Segment(B, D) → g_1
31. Segment(A, F) → h_1
32. Segment(C, F) → i_1
33. Segment(B, E) → j_1
34. Segment(C, E) → k_1
35. Midpoint(B, G) → I
36. Midpoint(A, G) → J
37. Midpoint(C, G) → K
38. Circle(H_{1}, Distance[H_{1}, a]) → d_1
39. Angle(B, C, H_{1}) → κ
40. Angle(A, C, H_{1}) → ι
41. Angle(B, A, H_{1}) → η
42. Angle(H_{1}, A, C) → θ
43. Angle(H_{1}, B, A) → μ
44. Angle(C, B, H_{1}) → λ