三条并发线段的构造与三角中心刻画

GeoGebra 命令及参数

1. Polygon(A, B, C) → t1, c, a, b
2. Rotate(B, α, C) → B'
3. Angle(B, C, B') → δ
4. Rotate(A, (-β), C) → A'
5. Angle(A', C, A) → ε
6. Ray(C, B') → f
7. Ray(C, A') → g
8. Rotate(C, γ, A) → C'
9. Angle(C, A, C') → ζ
10. Rotate(B, (-α), A) → B'_{1}
11. Angle(B'_{1}, A, B) → η
12. Ray(A, C') → h
13. Ray(A, B'_{1}) → i
14. Rotate(A, β, B) → A'_{1}
15. Angle(A, B, A'_{1}) → θ
16. Rotate(C, (-γ), B) → C'_{1}
17. Angle(C'_{1}, B, C) → ι
18. Ray(B, A'_{1}) → j
19. Ray(B, C'_{1}) → k
20. Intersect(h, g) → F
21. Intersect(i, j) → D
22. Intersect(f, k) → E
23. TriangleCenter(A, B, D, d) → H_1
24. TriangleCenter(B, C, E, d) → H_2
25. TriangleCenter(C, F, A, d) → H_3
26. Segment(B, H_2) → g_1
27. Segment(H_2, C) → h_1
28. Segment(C, H_3) → i_1
29. Segment(H_3, A) → j_1
30. Segment(A, H_1) → k_1
31. Segment(H_1, B) → l_1
32. Segment(C, F) → l
33. Segment(A, F) → m
34. Segment(C, E) → n
35. Segment(E, B) → p
36. Segment(B, D) → q
37. Segment(D, A) → r
38. Segment(A, H_2) → s
39. Segment(C, H_1) → t
40. Segment(H_3, B) → e
41. Intersect(s, t) → P
42. Angle(H_1, A, B) → κ
43. Angle(C, A, H_3) → λ
44. Angle(A, B, H_1) → μ
45. Angle(H_2, B, C) → ν
46. Angle(B, C, H_2) → ξ
47. Angle(H_3, C, A) → ο