外切与内切线段定理动态演示

GeoGebra 命令及参数

1. Circle(A, B) → c
2. Segment(A, B) → f
3. PointIn(a) → C
4. Distance(C, c) → b
5. Circle(C, d) → e
6. Tangent(c, e) → g, h, i, j
7. Intersect(c, h) → D
8. Intersect(c, j) → E, N
9. Intersect(e, j) → F
10. Intersect(e, h) → G, L
11. Intersect(e, g) → H, K
12. Intersect(e, i) → I
13. Intersect(c, i) → J, M
14. Intersect(c, g) → O
15. Circle(D, 2) → p
16. Circle(E, 2) → q
17. Circle(O, 2) → r
18. Circle(K, 2) → s
19. Circle(I, 2) → t
20. Circle(F, 2) → c_1
21. Circle(G, 2) → d_1
22. Circle(J, 2) → e_1
23. Intersect(e_1, i, 1) → P
24. Intersect(e_1, i, 2) → Q
25. Intersect(p, h, 1) → R
26. Intersect(p, h, 2) → S
27. Intersect(c_1, j, 2) → T
28. Intersect(c_1, j, 1) → U
29. Intersect(d_1, h, 1) → V
30. Intersect(d_1, h, 2) → W
31. Intersect(s, g, 2) → Z
32. Intersect(s, g, 1) → A_1
33. Intersect(r, g, 2) → B_1
34. Intersect(r, g, 1) → C_1
35. Intersect(q, j, 2) → D_1
36. Intersect(q, j, 1) → E_1
37. Dilate(A, If[0 < k ≤ 1, 1 - k, 0], D) → A'
38. Dilate(A, If[4 < k ≤ 5, 5 - k, 0], M) → A'_1
39. Dilate(A, If[9 < k ≤ 10, 10 - k, 0], E) → A'_2
40. Dilate(A, If[0 < k ≤ 1, 1 - k, 0], O) → A'_3
41. Angle(A, O, C_1) → α
42. Angle(A, E, E_1) → β
43. Angle(A, J, Q) → γ
44. Angle(A, D, S) → δ
45. Angle(C, K, A_1) → ε
46. Intersect(t, i, 1) → F_1
47. Angle(C, I, F_1) → ζ
48. Angle(C, F, T) → η
49. Angle(C, G, W) → θ
50. Dilate(C, If[0 < k ≤ 1, 1 - k, 0], G) → C'
51. Dilate(C, If[9 < k ≤ 10, 10 - k, 0], F) → C'_1
52. Dilate(C, If[4 < k ≤ 5, 5 - k, 0], I) → C'_2
53. Dilate(C, If[0 < k ≤ 1, 1 - k, 0], K) → C'_3
54. Segment(A, A') → l
55. Segment(A, A'_1) → m
56. Segment(A, A'_2) → n
57. Segment(A, A'_3) → f_1
58. Segment(C, C') → g_1
59. Segment(C, C'_1) → h_1
60. Segment(C, C'_2) → i_1
61. Segment(C, C'_3) → j_1
62. Intersect(i, j) → G_1
63. Intersect(i, j) → H_1
64. Intersect(h, i) → I_1
65. Intersect(g, j) → J_1
66. Intersect(g, i) → K_1
67. Intersect(h, j) → L_1
68. Segment(I_1, M) → k_1
69. Segment(M, I) → l_1
70. Segment(I, K_1) → m_1
71. Segment(J_1, E) → n_1
72. Segment(E, F) → p_1
73. Segment(F, L_1) → q_1
74. Dilate(K_1, If[1 < k ≤ 2, 2 - k, 0], M) → M_1
75. Dilate(M, If[2 < k ≤ 3, 3 - k, 0], I) → M'
76. Dilate(I, If[3 < k ≤ 4, 4 - k, 0], I_1) → I'
77. Segment(K_1, M_1) → r_1
78. Segment(M, M') → s_1
79. Segment(I, I') → t_1
80. Midpoint(M, I) → N_1
81. Rotate(K_1, If[5 < k ≤ 6, ((k - 5) * π), π], N_1) → O_1
82. Rotate(M_1, If[5 < k ≤ 6, ((k - 5) * π), π], N_1) → P_1
83. Segment(O_1, P_1) → a_1
84. Dilate(J_1, If[6 < k ≤ 7, 7 - k, 0], F) → Q_1
85. Dilate(F, If[7 < k ≤ 8, 8 - k, 0], E) → F'
86. Dilate(E, If[8 < k ≤ 9, 9 - k, 0], L_1) → E'
87. Segment(J_1, Q_1) → b_1
88. Segment(F, F') → f_2
89. Segment(E, E') → g_2
90. Midpoint(Q_1, E) → R_1
91. Rotate(J_1, If[10 < k ≤ 11, ((k - 10) * π), π], R_1) → S_1
92. Rotate(Q_1, If[10 < k ≤ 11, ((k - 10) * π), π], R_1) → T_1
93. Segment(S_1, T_1) → h_2
94. Dilate(L_1, If[11 < k ≤ 12, 12 - k, 0], I_1) → U_1
95. Vector(L_1, U_1) → u
96. Translate(S_1, u) → V_1
97. Translate(T_1, u) → W_1
98. Segment(V_1, W_1) → i_2
99. Line(I_1, f_2) → j_2
100. Point(j_2) → Z_1
101. Angle(Z_1, I_1, M') → ι
102. Rotate(V_1, If[12 < k ≤ 13, ((k - 12) * ι), ι], I_1) → A_2
103. Rotate(W_1, If[12 < k ≤ 13, ((k - 12) * ι), ι], I_1) → B_2
104. Segment(A_2, B_2) → k_2
105. Midpoint(E, M_1) → C_2
106. Rotate(S_1, If[13 < k ≤ 14, ((-(k - 13)) * π), (-π)], C_2) → D_2
107. Rotate(T_1, If[13 < k ≤ 14, ((-(k - 13)) * π), (-π)], C_2) → E_2
108. Segment(D_2, E_2) → l_2
109. Line(M_1, f_2) → m_2
110. Point(m_2) → F_2
111. Angle(K_1, M_1, F_2) → κ
112. Rotate(D_2, If[14 < k ≤ 15, ((-(k - 14)) * κ), (-κ)], M_1) → G_2
113. Rotate(E_2, If[14 < k ≤ 15, ((-(k - 14)) * κ), (-κ)], M_1) → H_2
114. Segment(G_2, H_2) → n_2