三角形的对称中心与对称补全

GeoGebra 命令及参数

1. Line(A, B) → a
2. Line(B, C) → b
3. Line(C, A) → c
4. Incircle(A, B, C) → d
5. AngularBisector(a, c) → e, f
6. AngularBisector(b, c) → g, h
7. AngularBisector(b, a) → i, j
8. Polygon(A, B, C) → poly1, c_1, a_1, b_1
9. Centroid(Polygon[A, B, C]) → D
10. Mirror(D, b_1) → D'
11. Mirror(D, a_1) → D'_1
12. Mirror(D, c_1) → D'_2
13. LineBisector(D'_2, D') → k
14. LineBisector(D', D'_1) → l
15. Intersect(k, l) → K
16. Circle(A, B, C) → p
17. OrthogonalLine(A, a_1) → m
18. OrthogonalLine(B, b_1) → n
19. OrthogonalLine(C, c_1) → q
20. Intersect(a, q) → E
21. Intersect(c, n) → F
22. Intersect(b, m) → G
23. Polygon(E, F, G) → poly2, g_1, e_1, f_1
24. Tangent(A, p) → r,
25. Tangent(B, p) → s,
26. Tangent(C, p) → t,
27. Intersect(r, s) → H
28. Intersect(r, t) → I
29. Intersect(s, t) → J
30. Polygon(H, I, J) → poly3, j_1, h_1, i_1
31. Line(H, E) → d_1
32. Line(I, F) → k_1
33. Line(J, G) → l_1
34. Intersect(d_1, k_1) → Q
35. Line(A, Q) → m_1
36. Line(Q, C) → n_1
37. Line(Q, B) → p_1
38. Line(K, A) → q_1
39. Line(K, C) → r_1
40. Line(K, B) → s_1
41. Intersect(c, s_1) → L
42. Intersect(b, q_1) → M
43. Intersect(b, m_1) → N
44. Intersect(c, p_1) → O
45. Intersect(a, r_1) → P
46. Intersect(a, n_1) → R
47. Mirror(M, K) → M'
48. Mirror(L, K) → L'
49. Mirror(P, K) → P'
50. Conic(M', O, L, P', M) → t_1