动态几何动画248：三角形内外心与旋转放缩的复合构造

GeoGebra 命令及参数

1. Line(A, B) → d
2. Slope(d) → a
3. PointIn(c) → C
4. Line(A, C) → e
5. Line(B, C) → f
6. Angle(B, A, C) → α
7. Angle(A, C, B) → β
8. Angle(C, B, A) → γ
9. Segment(A, C) → g
10. Segment(C, B) → h
11. Segment(B, A) → i
12. Min(list1) → j
13. Circle(C, (0.2 * j)) → q
14. Circle(A, (0.2 * j)) → p
15. Circle(B, (0.2 * j)) → k
16. Intersect(q, f, 2) → D
17. Intersect(q, e, 1) → E
18. Intersect(q, e, 2) → F
19. Intersect(p, e, 2) → G
20. Intersect(p, d, 1) → H
21. Intersect(k, f, 2) → I_2
22. Intersect(k, d, 2) → J
23. Intersect(d, i) → K
24. Intersect(d, i) → L
25. Intersect(k, f, 1) → N
26. Intersect(p, e, 1) → O
27. Intersect(p, d, 2) → P
28. Angle(D, C, E) → δ
29. Angle(O, A, P) → ε
30. Angle(J, B, I_2) → η
31. Angle(G, A, H) → θ
32. Incircle(A, B, C) → r
33. Center(r) → I
34. Line(C, I) → l
35. Line(A, I) → n
36. Line(B, I) → s
37. Intersect(e, s) → R
38. Intersect(d, l) → S
39. Intersect(f, n) → T
40. Polygon(A, B, C) → poly1, c_1, a_1, b_1
41. Rotate(D, δ / 2, C) → D'
42. Angle(D, C, D') → κ
43. Rotate(J, η / 2, B) → J'
44. Angle(J, B, J') → λ
45. Ray(C, D') → t
46. Ray(B, J') → e_1
47. Rotate(O, ε / 2, A) → O'
48. Angle(O, A, O') → ι
49. Ray(A, O') → d_1
50. Segment(C, S) → f_1
51. Segment(A, T) → g_1
52. Segment(B, R) → h_1
53. Intersect(q, f_1, 1) → U
54. Intersect(q, f, 1) → V
55. Intersect(p, g_1, 1) → W
56. Intersect(k, h_1, 1) → Z
57. CircleSector(A, P, W) → q_1
58. CircleSector(B, I_2, Z) → p_1
59. Dilate(C, If[0 < m ≤ 1, 1 - m, 0], S) → C'
60. Dilate(B, If[2 < m ≤ 3, 3 - m, 0], R) → B'
61. Segment(B, B') → j_1
62. Rotate(p_1, If[3 < m ≤ 4, ((m - 3) * γ / 2), γ / 2], B) → s_1
63. Dilate(A, If[4 < m ≤ 5, 5 - m, 0], T) → A'
64. Segment(A, A') → l_1
65. Rotate(q_1, If[5 < m ≤ 6, ((m - 5) * α / 2), α / 2], A) → t_1
66. OrthogonalLine(I, f) → m_1
67. OrthogonalLine(I, d) → n_1
68. OrthogonalLine(I, e) → a_2
69. Intersect(f, m_1) → M
70. Intersect(d, n_1) → A_1
71. Intersect(e, a_2) → B_1
72. Segment(I, M) → b_2
73. Circle(M, (0.2 * b_2)) → c_2
74. Intersect(c_2, f, 1) → C_1
75. Intersect(c_2, b_2, 1) → D_1
76. Intersect(c_2, f, 2) → E_1
77. CircleSector(M, E_1, D_1) → d_2
78. Dilate(I, If[6 < m ≤ 7, 7 - m, 0], M) → Q'
79. Segment(I, Q') → e_2
80. Rotate(d_2, If[7.5 < m ≤ 8.5, ((m - 7.5) * π / 2), 1.5707963267948966], M) → f_2
81. Segment(I, B_1) → g_2
82. Segment(I, A_1) → h_2
83. Circle(B_1, (0.2 * g_2)) → k_2
84. Circle(A_1, (0.2 * h_2)) → p_2
85. Intersect(k_2, e, 2) → F_1
86. Intersect(k_2, g_2, 1) → G_1
87. Intersect(k_2, e, 1) → H_1
88. Intersect(p_2, d, 2) → I_1
89. Intersect(p_2, h_2, 1) → J_1
90. Intersect(p_2, d, 1) → K_1
91. Dilate(I, If[8.5 < m ≤ 9.5, 9.5 - m, 0], B_1) → Q'_1
92. Segment(I, Q'_1) → i_2
93. CircleSector(B_1, H_1, G_1) → q_2
94. CircleSector(A_1, I_1, J_1) → r_2
95. Rotate(q_2, If[10 < m ≤ 11, ((m - 10) * π / 2), 1.5707963267948966], B_1) → s_2
96. Dilate(I, If[11 < m ≤ 12, 12 - m, 0], A_1) → Q'_2
97. Segment(I, Q'_2) → j_2
98. Rotate(r_2, If[12.5 < m ≤ 13.5, ((m - 12.5) * π / 2), 1.5708], A_1) → t_2
99. Angle(M, I, B_1) → ζ
100. Angle(B_1, I, A_1) → μ
101. Angle(A_1, I, M) → ν
102. Rotate(I, If[14 < m ≤ 15, ((m - 14) * ζ), ζ], I) → Q'_3
103. Rotate(Q', If[14 < m ≤ 15, ((m - 14) * ζ), ζ], I) → Q''
104. Segment(Q'_3, Q'') → l_2
105. Rotate(Q'_3, If[15 < m ≤ 16, ((m - 15) * μ), μ], I) → L_1
106. Rotate(Q'', If[15 < m ≤ 16, ((m - 15) * μ), μ], I) → Q'''
107. Segment(L_1, Q''') → m_2
108. Rotate(A_1, If[16 < m ≤ 18, ((m - 16) * π), 6.28319], I) → M'
109. Intersect(m_1, f) → Q
110. Circle(I, Q) → d_3
111. Line(A, B) → n_2
112. CircleArc(I, A_1, M') → c_3
113. Circle(A, I, B) → k_1
114. LineBisector(I, B) → i_1
115. LineBisector(I, A) → r_1
116. Intersect(i_1, r_1) → M_1
117. Dilate(M_1, If[19 < m ≤ 20, 20 - m, 0], B) → N_1
118. Segment(M_1, N_1) → f_3
119. Rotate(B, If[20 < m ≤ 22, ((m - 20) * π), (2 * π)], M_1) → B'_1
120. CircleArc(M_1, B, B'_1) → e_3
121. Dilate(C, If[22 < m ≤ 23, 23 - m, 0], I) → C'_1
122. Segment(C, C'_1) → g_3
123. Dilate(I, If[23 < m ≤ 24, 24 - m, 0], M_1) → I'
124. Segment(I, I') → h_3