圆与三角形的几何构造

GeoGebra 命令及参数

1. Segment((0, 0), (r, 0)) → f
2. Rotate((r, 0), 1, (0, 0)) → A
3. Rotate((r, 0), 2, (0, 0)) → B
4. Rotate((r, 0), 3, (0, 0)) → C
5. Rotate((r, 0), 4, (0, 0)) → D
6. Rotate((r, 0), 5, (0, 0)) → E
7. Rotate((r, 0), -1, (0, 0)) → F
8. Rotate(f, If[0 < a ≤ 1, ((-a) * pi / 2), ((-pi)) / 2], (r, 0)) → f'
9. Rotate(G, If[1.5 < a ≤ 2.5, a - 1.5, 1], (0, 0)) → G'
10. CircleArc((0, 0), G, G') → c
11. Circle(G', r - c) → d
12. Line((0, 0), G') → g
13. OrthogonalLine(G', g) → h
14. Intersect(d, h, 2) → H
15. Segment(G', H) → i
16. Dilate(G, If[3 < a ≤ 4, 4 - a, 0], A) → G'_{1}
17. Vector(G, G'_{1}) → u
18. Translate(f, u) → f'_{1}
19. Line((0, 0), A) → j
20. OrthogonalLine(A, j) → k
21. Point(p) → I
22. Point(k) → J
23. Angle(J, A, I) → α
24. Rotate(f'_{1}, If[3 < a ≤ 4, ((-(a - 3)) * α), (-α)], G'_{1}) → l
25. Rotate(A, If[4 < a ≤ 5, a - 4, 1], (0, 0)) → A'
26. CircleArc((0, 0), A, A') → e
27. Circle(A', r - e) → q
28. Line((0, 0), A') → m
29. OrthogonalLine(A', m) → n
30. Intersect(q, n, 2) → K
31. Segment(A', K) → s
32. Dilate((0, 0), If[5.5 < a ≤ 6.5, 6.5 - a, 0], B) → L
33. Vector(M, L) → v
34. Translate(f, v) → f'_{2}
35. Line(M, B) → b
36. OrthogonalLine(B, b) → f_1
37. Point(t) → N
38. Point(f_1) → O
39. Angle(O, B, N) → β
40. Rotate(f'_{2}, If[5.5 < a ≤ 6.5, ((-(a - 5.5)) * β), (-β)], L) → g_1
41. Rotate(B, If[6.5 < a ≤ 7.5, a - 6.5, 1], (0, 0)) → B'
42. CircleArc(M, B, B') → c_1
43. Line(M, B') → h_1
44. OrthogonalLine(B', h_1) → i_1
45. Circle(B', r - c_1) → d_1
46. Intersect(d_1, i_1, 2) → P
47. Dilate(M, If[8 < a ≤ 9, 9 - a, 0], C) → M'
48. Vector(M, M') → w
49. Translate(f, w) → f'_{3}
50. Line(M, C) → k_1
51. OrthogonalLine(C, k_1) → l_1
52. Point(p_1) → Q
53. Point(l_1) → R
54. Angle(R, C, Q) → γ
55. Rotate(f'_{3}, If[8 < a ≤ 9, ((-(a - 8)) * γ), (-γ)], M') → m_1
56. Rotate(C, If[9 < a ≤ 10, a - 9, 1], M) → C'
57. CircleArc(M, C, C') → e_1
58. Line(M, C') → n_1
59. OrthogonalLine(C', n_1) → q_1
60. Circle(C', r - e_1) → r_1
61. Intersect(r_1, q_1) → S, B_1
62. Intersect(d_1, i_1, 1) → T
63. Dilate(M, If[10.5 < a ≤ 11.5, 11.5 - a, 0], D) → M'_{1}
64. Vector(M, M'_{1}) → u_1
65. Translate(f, u_1) → f'_{4}
66. Line(M, D) → a_1
67. OrthogonalLine(D, a_1) → b_1
68. Point(b_1) → U
69. Point(t_1) → V
70. Angle(U, D, V) → δ
71. Rotate(f'_{4}, If[10.5 < a ≤ 11.5, ((-(a - 10.5)) * δ), (-δ)], M'_{1}) → f_2
72. Rotate(D, If[11.5 < a ≤ 12.5, a - 11.5, 1], M) → D'
73. CircleArc(M, D, D') → c_2
74. Line(M, D') → g_2
75. OrthogonalLine(D', g_2) → h_2
76. Circle(D', r - c_2) → d_2
77. Intersect(d_2, h_2, 2) → W
78. Segment(D', W) → i_2
79. Intersect(d_2, h_2, 1) → Z
80. Rotate(M, If[13 < a ≤ 14, ((a - 13) * pi / 2), pi / 2], G) → M'_{2}
81. Segment(G, M'_{2}) → j_2
82. If(x(P) ≤ x(T), P, T) → A_1
83. Segment(B', A_1) → j_1
84. If(y(B_1) < y(S), B_1, S) → C_1
85. Segment(C', C_1) → s_1
86. Rotate(G, If[14 < a ≤ 15, (-(a - 14)), -1], M) → G'_{2}
87. CircleArc(M, G'_{2}, G) → e_2
88. Line(M, G'_{2}) → k_2
89. Circle(G'_{2}, r - e_2) → p_2
90. OrthogonalLine(G'_{2}, k_2) → l_2
91. Intersect(p_2, l_2) → D_1, E_1
92. If(y(D_1) ≤ y(E_1), D_1, E_1) → F_1
93. Segment(G'_{2}, F_1) → m_2
94. Rotate(D, 1, M) → D'_{1}
95. Rotate(G, 0.5) → G'_{3}
96. Rotate(G, 1.5) → G'_{4}
97. Rotate(G, 2.5) → G'_{5}
98. Rotate(G, 3.5) → G'_{6}
99. Rotate(G, 4.5) → G'_{7}
100. Rotate(G, -0.5) → G'_{8}
101. Segment(G_1, G) → n_2
102. Circle(G_1, n_2 / 7) → q_2
103. Intersect(q_2, n_2, 1) → H_1
104. Mirror(G_1, H_1) → I_1
105. Mirror(H_1, I_1) → J_1
106. Mirror(I_1, J_1) → K_1
107. Mirror(J_1, K_1) → L_1
108. Mirror(K_1, L_1) → M_1
109. Dilate(G_1, If[16 < a ≤ 17, 17 - a, 0], H_1) → N_1
110. Segment(G_1, N_1) → r_2
111. Rotate(G_1, If[17 < a ≤ 18, ((a - 17) * pi), pi], H_1) → O_1
112. Rotate(N_1, If[17 < a ≤ 18, ((a - 17) * pi), pi], H_1) → P_1
113. Segment(O_1, P_1) → s_2
114. Rotate(O_1, If[18 < a ≤ 19, ((a - 18) * pi), pi], I_1) → Q_1
115. Rotate(P_1, If[18 < a ≤ 19, ((a - 18) * pi), pi], I_1) → R_1
116. Segment(Q_1, R_1) → t_2
117. Rotate(Q_1, If[19 < a ≤ 20, ((a - 19) * pi), pi], J_1) → S_1
118. Rotate(R_1, If[19 < a ≤ 20, ((a - 19) * pi), pi], J_1) → T_1
119. Segment(S_1, T_1) → a_2
120. Rotate(S_1, If[20 < a ≤ 21, ((a - 20) * pi), pi], K_1) → U_1
121. Rotate(T_1, If[20 < a ≤ 21, ((a - 20) * pi), pi], K_1) → V_1
122. Segment(U_1, V_1) → b_2
123. Rotate(U_1, If[21 < a ≤ 22, ((a - 21) * pi), pi], L_1) → W_1
124. Rotate(V_1, If[21 < a ≤ 22, ((a - 21) * pi), pi], L_1) → Z_1
125. Segment(W_1, Z_1) → f_3
126. Rotate(W_1, If[22 < a ≤ 23, ((a - 22) * pi), pi], M_1) → A_2
127. Rotate(Z_1, If[22 < a ≤ 23, ((a - 22) * pi), pi], M_1) → B_2
128. Segment(A_2, B_2) → g_3
129. Dilate(I_1, If[24 < a ≤ 25, 25 - a, 0], F) → C_2
130. Vector(I_1, C_2) → v_1
131. Translate(O_1, v_1) → D_2
132. Translate(P_1, v_1) → E_2
133. Segment(D_2, E_2) → h_3
134. Translate(G_1, v_1) → F_2
135. Translate(N_1, v_1) → G_2
136. Segment(F_2, G_2) → i_3
137. Line(G_1, F) → j_3
138. OrthogonalLine(F, j_3) → k_3
139. Line(F, n_2) → l_3
140. Point(l_3) → H_2
141. Point(k_3) → I_2
142. Angle(H_2, F, I_2) → ε
143. Rotate(D_2, If[24 < a ≤ 25, ((a - 24) * ε), ε], D_2) → J_2
144. Rotate(E_2, If[24 < a ≤ 25, ((a - 24) * ε), ε], D_2) → K_2
145. Rotate(F_2, If[24 < a ≤ 25, ((a - 24) * ε), ε], D_2) → L_2
146. Rotate(G_2, If[24 < a ≤ 25, ((a - 24) * ε), ε], D_2) → M_2
147. Segment(J_2, L_2) → m_3
148. Rotate(F, If[25 < a ≤ 26, ((-(a - 25)) * ((2 * pi) - 6)), 6 - (2 * pi)], G_1) → F'
149. CircleArc(G_1, F', F) → c_3
150. Line(G_1, F') → n_3
151. OrthogonalLine(F', n_3) → p_3
152. Intersect(p_3, eq3) → N_2
153. Ray(F', N_2) → q_3
154. Point(q_3) → O_2
155. CircleArc(G_1, D'_{1}, F) → d_3
156. Circle(F', d_3 - c_3) → e_3
157. Intersect(e_3, q_3, 1) → P_2
158. Segment(F', P_2) → r_3