欧拉线：三角形中的重要几何关系

GeoGebra 命令及参数

1. Polygon(A, B, C) → t1, c, a, b
2. Vector(A, E) → v
3. Vector(A, F) → w
4. Translate(A, v) → A'_{1}
5. Translate(B, v) → B'_{1}
6. Translate(C, v) → C'_{1}
7. Polygon(A'_{1}, B'_{1}, C'_{1}) → t1'_{1}, c'_{1}, a'_{1}, b'_{1}
8. Translate(A, w) → A'_{2}
9. Translate(B, w) → B'_{2}
10. Translate(C, w) → C'_{2}
11. Polygon(A'_{2}, B'_{2}, C'_{2}) → t1'_{2}, c'_{2}, a'_{2}, b'_{2}
12. Midpoint(b'_{1}) → G
13. Midpoint(a'_{1}) → H
14. Midpoint(c'_{1}) → I
15. Segment(B'_{1}, G) → i
16. Segment(I, C'_{1}) → j
17. Segment(H, E) → k
18. Intersect(j, k) → J
19. Vector(A, D) → u
20. Translate(A, u) → A'
21. Translate(B, u) → B'
22. Translate(C, u) → C'
23. Polygon(A', B', C') → t1', c', a', b'
24. LineBisector(a') → f
25. LineBisector(b') → g
26. LineBisector(c') → h
27. Intersect(f, a') → K
28. Intersect(c', h) → L
29. Intersect(g, b') → M
30. Intersect(f, g) → N
31. Circle(N, B') → d
32. Intersect(d, h) → O, P
33. Intersect(d, f) → Q, R
34. Intersect(d, g) → S, T
35. Segment(P, O) → l
36. Segment(Q, R) → m
37. Segment(S, T) → n
38. Angle(Q, K, C') → α
39. Angle(C', M, S) → β
40. Angle(A', L, O) → γ
41. Segment(E, G) → p
42. Segment(G, C'_{1}) → q
43. Segment(E, I) → r
44. Segment(I, B'_{1}) → s
45. Segment(B'_{1}, H) → t
46. Segment(H, C'_{1}) → e
47. Segment(D, L) → f_1
48. Segment(L, B') → g_1
49. Segment(B', K) → h_1
50. Segment(K, C') → i_1
51. Segment(C', M) → j_1
52. Segment(M, D) → k_1
53. Line(F, C'_{2}) → l_1
54. Line(B'_{2}, C'_{2}) → m_1
55. Line(B'_{2}, F) → n_1
56. OrthogonalLine(B'_{2}, l_1) → p_1
57. OrthogonalLine(F, m_1) → q_1
58. OrthogonalLine(C'_{2}, n_1) → r_1
59. Intersect(n_1, r_1) → U
60. Intersect(q_1, m_1) → V
61. Intersect(p_1, l_1) → W
62. Segment(B'_{2}, W) → s_1
63. Segment(C'_{2}, U) → t_1
64. Segment(F, V) → a_1
65. Segment(C'_{2}, W) → b_1
66. Segment(C'_{2}, V) → c_1
67. Segment(F, U) → d_1
68. Angle(C'_{2}, W, B'_{2}) → δ
69. Angle(C'_{2}, U, B'_{2}) → ε
70. Angle(F, V, C'_{2}) → ζ
71. Intersect(a_1, s_1) → Z
72. Intersect(t1, t1'_{2}) → A_1
73. LineBisector(b) → e_1
74. LineBisector(a) → f_2
75. Intersect(f_2, e_1) → B_1
76. Midpoint(a) → C_1
77. Midpoint(b) → D_1
78. Segment(B, D_1) → g_2
79. Segment(C_1, A) → h_2
80. Intersect(h_2, g_2) → E_1
81. Line(A, C) → i_2
82. Line(B, C) → j_2
83. OrthogonalLine(A, j_2) → k_2
84. OrthogonalLine(B, i_2) → l_2
85. Intersect(k_2, l_2) → F_1
86. Circle(B_1, B) → c_2
87. Line(B_1, F_1) → m_2
88. Intersect(c_2, m_2) → G_1, H_1
89. Segment(G_1, H_1) → n_2
90. Intersect(k, i) → I_1
91. Segment(E_1, F_1) → p_2
92. Midpoint(c) → L_1
93. Vector(C' + (0.5, -0.5), L_1 - (1, -0.5)) → u_1
94. Midpoint(a) → M_1
95. Vector(F - (0.5, 0.5), M_1 + (0.5, 0.5)) → v_1
96. Vector(G - (0, 0.5), B + (-0.25, 0.5)) → w_1