三角形内接圆与角平分线的比例关系构造

GeoGebra 命令及参数

1. Polygon(A, B, C) → d1, c, a, b
2. Line(A, B) → f
3. Line(C, B) → g
4. Line(A, C) → h
5. LineBisector(A, B) → i
6. LineBisector(C, B) → j
7. Intersect(i, j) → U
8. LineBisector(A, U) → k
9. Intersect(h, k) → D
10. Intersect(f, k) → E
11. Polygon(D, E, U) → d2, u, d, e
12. Segment(A, E) → l
13. Segment(A, D) → m
14. Segment(D, C) → p
15. Segment(E, B) → q
16. Midpoint(A, B) → F
17. Midpoint(C, A) → G
18. Segment(G, B) → r
19. Segment(F, C) → s
20. Intersect(r, s) → S
21. Segment(U, C) → t
22. Segment(U, B) → f_1
23. Segment(U, A) → g_1
24. Midpoint(C, B) → H_{1}
25. Segment(S, H_{1}) → h_1
26. Segment(S, F) → i_1
27. Segment(G, S) → j_1
28. LineBisector(A, S) → k_1
29. Intersect(h, k_1) → I_{1}
30. Intersect(f, k_1) → J
31. Polygon(I_{1}, J, S) → d3, s_1, i_2, j_2
32. Segment(A, J) → l_1
33. Segment(A, I_{1}) → m_1
34. Segment(I_{1}, C) → n_1
35. Segment(J, B) → p_1
36. Incircle(A, B, C) → c_1
37. Center(c_1) → I
38. Intersect(c_1, h, 1) → L
39. Intersect(c_1, f, 1) → M
40. Intersect(c_1, g, 1) → N
41. Segment(I, N) → q_1
42. Segment(I, L) → r_1
43. Segment(I, M) → t_1
44. LineBisector(A, I) → a_1
45. Intersect(f, a_1) → K
46. Intersect(h, a_1) → O
47. Polygon(O, K, I) → d4, i_3, o, k_2
48. Segment(A, O) → b_1
49. Segment(A, K) → d_1
50. Segment(O, C) → e_1
51. Segment(K, B) → f_2
52. OrthogonalLine(B, h) → g_2
53. OrthogonalLine(C, f) → h_2
54. Intersect(h_2, f) → P
55. Intersect(g_2, h) → Q
56. Intersect(g_2, h_2) → H
57. OrthogonalLine(A, g) → l_2
58. Intersect(g, l_2) → T
59. Segment(C, P) → m_2
60. Segment(A, T) → n_2
61. Segment(Q, B) → p_2
62. LineBisector(A, H) → q_2
63. Intersect(q_2, h) → R
64. Intersect(q_2, f) → V
65. Polygon(R, V, H) → d5, h_3, r_2, v
66. Segment(A, V) → s_2
67. Segment(V, B) → t_2
68. Segment(A, R) → a_2
69. Segment(R, C) → b_2