欧拉线惊喜：特殊等腰三角形动态演示

GeoGebra 命令及参数

1. Line(A, B) → f
2. Rotate(B, π / 3, A) → B'
3. Angle(B, A, B') → α
4. Rotate(B', π / 3, A) → B''
5. Angle(B', A, B'') → β
6. Ray(A, B'') → g
7. Ray(A, B') → h
8. Point(h) → C
9. Mirror(B, A) → B'_1
10. Ray(A, B) → j
11. Point(j) → D
12. Segment(C, D) → i
13. Ray(A, B'_1) → k
14. Segment(A, D) → l
15. Segment(A, C) → m
16. Circle(A, (0.15 * Min[l, m])) → c
17. Intersect(c, k, 1) → E
18. Intersect(c, g) → F,
19. CircleSector(A, F, E) → d
20. Rotate(d, If[0 < a ≤ 1, ((-a) * π / 3), ((-π)) / 3], A) → d'
21. Rotate(d', If[2 < a ≤ 3, ((-(a - 2)) * π / 3), ((-π)) / 3], A) → d''
22. Polygon(A, C, D) → poly1, d_1, a_1, c_1
23. Midpoint(A, D) → G
24. Midpoint(A, C) → I
25. Line(A, C) → n
26. OrthogonalLine(D, n) → p
27. Intersect(n, p) → J
28. Line(A, D) → q
29. OrthogonalLine(C, q) → r
30. Intersect(r, q) → H
31. Dilate(A, If[3 < a ≤ 4, 4 - a, 0], G) → A'
32. Dilate(A, If[3 < a ≤ 4, 4 - a, 0], I) → A'_1
33. Segment(A, A') → s
34. Segment(A, A'_1) → t
35. Rotate(A, If[4 < a ≤ 5, ((-(a - 4)) * π), (-π)], G) → A'_2
36. Rotate(A', If[4 < a ≤ 5, ((-(a - 4)) * π), (-π)], G) → A''
37. Segment(A'_2, A'') → s'
38. Rotate(A, If[4 < a ≤ 5, ((-(a - 4)) * π), (-π)], I) → A'_3
39. Rotate(A'_1, If[4 < a ≤ 5, ((-(a - 4)) * π), (-π)], I) → K
40. Segment(A'_3, K) → t'
41. Line(C, G) → b
42. Line(D, I) → e
43. Intersect(b, e) → L
44. Intersect(p, r) → M
45. Dilate(D, If[5 < a ≤ 6, 6 - a, 0], L) → D'
46. Dilate(C, If[5 < a ≤ 6, 6 - a, 0], L) → C'
47. Segment(C, C') → f_1
48. Segment(D, D') → g_1
49. Dilate(L, If[6 < a ≤ 7, 7 - a, 0], G) → L'
50. Dilate(L, If[6 < a ≤ 7, 7 - a, 0], I) → L'_1
51. Segment(L, L'_1) → h_1
52. Segment(L, L') → i_1
53. Dilate(C, If[7 < a ≤ 8, 8 - a, 0], M) → C'_1
54. Dilate(D, If[7 < a ≤ 8, 8 - a, 0], M) → D'_1
55. Segment(C, C'_1) → j_1
56. Segment(D, D'_1) → k_1
57. Angle(D, J, C) → γ
58. Angle(D, H, C) → δ
59. Dilate(M, If[8 < a ≤ 9, 9 - a, 0], J) → M'
60. Dilate(M, If[8 < a ≤ 9, 9 - a, 0], H) → M'_1
61. Segment(M, M') → l_1
62. Segment(M, M'_1) → m_1
63. Line(A, C) → n_1
64. Circle(C, 1) → e_1
65. Intersect(e_1, n_1, 2) → N
66. Circle(A, 1) → p_1
67. Intersect(p_1, n_1) → O, P
68. Ray(C, N) → q_1
69. Ray(A, O) → r_1
70. Ray(A, D) → s_1
71. Circle(D, 1) → t_1
72. Intersect(t_1, s_1) → Q, R
73. Ray(D, R) → b_1
74. Line(M, L) → f_2
75. Intersect(n, f_2) → S
76. Intersect(q, f_2) → T
77. Dilate(M, If[9 < a ≤ 10, 10 - a, 0], L) → M'_2
78. Segment(M, M'_2) → g_2
79. Polygon(A, T, S) → poly2, s_2, a_2, t_2
80. Segment(S, C) → h_2
81. Segment(T, D) → i_2
82. Dilate(A, If[12 < a ≤ 13, 13 - a, 0], T) → A'_4
83. Vector(A, A'_4) → u
84. Translate(d'', u) → d'''
85. Rotate(d''', If[13 < a ≤ 14, (((a - 13) * 2) * π / 3), (2 * π / 3)], T) → c_2
86. Dilate(T, If[14 < a ≤ 15, 15 - a, 0], S) → T'
87. Vector(T, T') → v
88. Translate(c_2, v) → d_2
89. Rotate(d_2, If[15 < a ≤ 16, (((a - 15) * 2) * π / 3), (2 * π / 3)], S) → e_2