圆内接正方形面积问题动态演示

GeoGebra 命令及参数

1. Polygon(A, B, 4) → poly1, f, g, h, i, C, D
2. LineBisector(A, B) → j
3. LineBisector(C, B) → k
4. Intersect(k, j) → E
5. Intersect(j, h) → F
6. Circle(E, F) → c
7. Intersect(g, k) → G
8. Segment(B, F) → l
9. Segment(A, G) → m
10. Intersect(c, l) → H, I
11. Segment(G, I) → n
12. Intersect(l, m) → J
13. Segment(G, J) → p
14. Segment(J, I) → q
15. Segment(D, A) → r
16. Segment(C, B) → s
17. Segment(B, A) → t
18. Segment(I, B) → d
19. Intersect(k, l) → K
20. Segment(J, K) → e
21. Line(E, l) → f_1
22. Intersect(f_1, t) → L
23. Intersect(f_1, m) → M
24. Segment(K, G) → h_1
25. Segment(E, K) → i_1
26. Segment(D, C) → j_1
27. Intersect(j, m) → N
28. Intersect(c, r) → O, S
29. Dilate(A, If[0 < u ≤ 1, 1 - u, 0], G) → A'
30. Segment(A, A') → g_1
31. Dilate(O, If[0 < u ≤ 1, 1 - u, 0], G) → O'
32. Segment(O, O') → k_1
33. Dilate(F, If[1 < u ≤ 2, 2 - u, 0], K) → F'
34. Segment(F, F') → l_1
35. Dilate(K, If[2 < u ≤ 3, 3 - u, 0], J) → K'
36. Segment(K, K') → m_1
37. Midpoint(J, I) → P
38. Intersect(c, t) → Q, T
39. Dilate(F, If[0 < u ≤ 1, 1 - u, 0], Q) → F'_1
40. Segment(F, F'_1) → n_1
41. Dilate(J, If[3 < u ≤ 4, 4 - u, 0], P) → J'
42. Segment(J, J') → p_1
43. Dilate(P, If[4 < u ≤ 5, 5 - u, 0], I) → P'
44. Segment(P, P') → q_1
45. Dilate(G, If[4 < u ≤ 5, 5 - u, 0], I) → G'
46. Segment(G, G') → r_1
47. Dilate(I, If[5 < u ≤ 6, 6 - u, 0], B) → I'
48. Polygon(I, J, G) → poly2, g_2, i_2, j_2
49. Polygon(K, J, G) → poly3, g_3, k_2, j_3
50. Rotate(K, If[7 < u ≤ 8, ((u - 7) * π), π], J) → K'_1
51. Rotate(K', If[7 < u ≤ 8, ((u - 7) * π), π], J) → K''
52. Segment(K'_1, K'') → t_1
53. Rotate(K'_1, If[8 < u ≤ 9, ((u - 8) * π), π], P) → R
54. Rotate(K'', If[8 < u ≤ 9, ((u - 8) * π), π], P) → K'''
55. Segment(R, K''') → a_1
56. Dilate(J, If[10 < u ≤ 11, 11 - u, 0], I) → J'_1
57. Midpoint(I, B) → U
58. Dilate(I, If[5 < u ≤ 6, 6 - u, 0], U) → I'_1
59. Segment(I, I'_1) → s_1
60. Dilate(U, If[6 < u ≤ 7, 7 - u, 0], B) → U'
61. Segment(U, U') → b_1
62. Polygon(I, B, G) → poly4, g_4, i_3, b_2
63. Rotate(R, If[9 < u ≤ 10, ((u - 9) * π), π], I) → R'
64. Rotate(K''', If[9 < u ≤ 10, ((u - 9) * π), π], I) → V
65. Segment(R', V) → c_1
66. Rotate(R', If[10 < u ≤ 11, ((u - 10) * π), π], U) → R''
67. Rotate(V, If[10 < u ≤ 11, ((u - 10) * π), π], U) → V'
68. Segment(R'', V') → d_1
69. Midpoint(K, B) → W
70. Rotate(K, If[12 < u ≤ 13, ((u - 12) * π), π], W) → K'_2
71. Rotate(J, If[12 < u ≤ 13, ((u - 12) * π), π], W) → J'_2
72. Rotate(G, If[12 < u ≤ 13, ((u - 12) * π), π], W) → G'_1
73. Polygon(K'_2, J'_2, G'_1) → poly3', g'_1, k'_2, j'_2
74. Rotate(I, If[12 < u ≤ 13, ((u - 12) * π), π], W) → I'_2
75. Rotate(J, If[12 < u ≤ 13, ((u - 12) * π), π], W) → J'_3
76. Rotate(G, If[12 < u ≤ 13, ((u - 12) * π), π], W) → G'_2
77. Polygon(I'_2, J'_3, G'_2) → poly2', g'_2, i'_2, j'_3
78. Rotate(I, If[12 < u ≤ 13, ((u - 12) * π), π], W) → I'_3
79. Rotate(B, If[12 < u ≤ 13, ((u - 12) * π), π], W) → B'
80. Rotate(G, If[12 < u ≤ 13, ((u - 12) * π), π], W) → G'_3
81. Polygon(I'_3, B', G'_3) → poly4', g'_3, i'_3, b'
82. Dilate(E, If[16 < u ≤ 17, 17 - u, 0], D) → K'_3
83. Vector(E, K'_3) → v
84. Dilate(L, If[13 < u ≤ 14, 14 - u, 0], Q) → L'
85. Vector(L, L') → w
86. Translate(I'_3, w) → Z
87. Translate(B', w) → B''
88. Translate(G'_3, w) → A_1
89. Polygon(Z, B'', A_1) → poly4'', a_2, z_1, b''
90. Translate(I'_2, w) → B_1
91. Translate(J'_3, w) → C_1
92. Translate(G'_2, w) → D_1
93. Polygon(B_1, C_1, D_1) → poly2'', d_2, b_3, c_2
94. Translate(K'_2, w) → E_1
95. Translate(J'_2, w) → F_1
96. Translate(G'_1, w) → G_1
97. Polygon(E_1, F_1, G_1) → poly3'', g_5, e_1, f_2
98. Midpoint(E, L) → H_1
99. Rotate(B_1, If[14 < u ≤ 15, ((u - 14) * π), π], H_1) → I_1
100. Rotate(C_1, If[14 < u ≤ 15, ((u - 14) * π), π], H_1) → J_1
101. Rotate(D_1, If[14 < u ≤ 15, ((u - 14) * π), π], H_1) → K_1
102. Polygon(I_1, J_1, K_1) → poly2''', k_3, i_4, j_4
103. Rotate(Z, If[14 < u ≤ 15, ((u - 14) * π), π], H_1) → Z'
104. Rotate(B'', If[14 < u ≤ 15, ((u - 14) * π), π], H_1) → B'''
105. Rotate(A_1, If[14 < u ≤ 15, ((u - 14) * π), π], H_1) → L_1
106. Polygon(Z', B''', L_1) → poly4''', l_2, z', b'''
107. Rotate(E_1, If[14 < u ≤ 15, ((u - 14) * π), π], H_1) → M_1
108. Rotate(F_1, If[14 < u ≤ 15, ((u - 14) * π), π], H_1) → N_1
109. Rotate(G_1, If[14 < u ≤ 15, ((u - 14) * π), π], H_1) → O_1
110. Polygon(M_1, N_1, O_1) → poly3''', o_1, m_2, n_2
111. Dilate(Q, If[16 < u ≤ 17, 17 - u, 0], A) → Q'
112. Vector(Q, Q') → u_1
113. Vector(P_1, Q_1) → v_1
114. Dilate(E, If[16 < u ≤ 17, 17 - u, 0], F) → E'
115. Vector(E, E') → w_1
116. Translate(Z, u_1) → Z'_1
117. Translate(B'', u_1) → B'''_1
118. Translate(A_1, u_1) → R_1
119. Polygon(Z'_1, B'''_1, R_1) → poly4'''_1, r_2, z'_1, b'''_1
120. Translate(Z, w_1) → Z'_2
121. Translate(B'', w_1) → B'''_2
122. Translate(A_1, w_1) → S_1
123. Polygon(Z'_2, B'''_2, S_1) → poly4'''_2, s_2, z'_2, b'''_2
124. Translate(Z, v) → Z'_3
125. Translate(B'', v) → B'''_3
126. Translate(A_1, v) → T_1
127. Polygon(Z'_3, B'''_3, T_1) → poly4'''_3, t_2, z'_3, b'''_3
128. Translate(B_1, v) → U_1
129. Translate(C_1, v) → V_1
130. Translate(D_1, v) → W_1
131. Polygon(U_1, V_1, W_1) → poly2'''_1, w_2, u_2, v_2
132. Translate(B_1, u_1) → Z_1
133. Translate(C_1, u_1) → A_2
134. Translate(D_1, u_1) → B_2
135. Polygon(Z_1, A_2, B_2) → poly2'''_2, b_4, z_2, a_3
136. Translate(B_1, w_1) → C_2
137. Translate(C_1, w_1) → D_2
138. Translate(D_1, w_1) → E_2
139. Polygon(C_2, D_2, E_2) → poly2'''_3, e_2, c_3, d_3
140. Translate(E_1, u_1) → F_2
141. Translate(F_1, u_1) → G_2
142. Translate(G_1, u_1) → H_2
143. Polygon(F_2, G_2, H_2) → poly3'''_1, h_2, f_3, g_6
144. Translate(E_1, v) → I_2
145. Translate(F_1, v) → J_2
146. Translate(G_1, v) → K_2
147. Polygon(I_2, J_2, K_2) → poly3'''_2, k_4, i_5, j_5
148. Translate(E_1, w_1) → L_2
149. Translate(F_1, w_1) → M_2
150. Translate(G_1, w_1) → N_2
151. Polygon(L_2, M_2, N_2) → poly3'''_3, n_3, l_3, m_3
152. Translate(Z', u_1) → Z''
153. Translate(B''', u_1) → O_2
154. Translate(L_1, u_1) → P_2
155. Polygon(Z'', O_2, P_2) → poly5, p_2, z'', o_2
156. Translate(I_1, u_1) → Q_2
157. Translate(J_1, u_1) → R_2
158. Translate(K_1, u_1) → S_2
159. Polygon(Q_2, R_2, S_2) → poly6, s_3, q_2, r_3
160. Translate(M_1, u_1) → T_2
161. Translate(N_1, u_1) → U_2
162. Translate(O_1, u_1) → V_2
163. Polygon(T_2, U_2, V_2) → poly7, v_3, t_3, u_3
164. Translate(I'_3, u_1) → W_2
165. Translate(B', u_1) → B''_1
166. Translate(G'_3, u_1) → Z_2
167. Polygon(W_2, B''_1, Z_2) → poly4''_1, z_3, w_3, b''_1
168. Translate(K, u_1) → K'_4
169. Translate(J, u_1) → J'_4
170. Translate(G, u_1) → G'_4
171. Polygon(K'_4, J'_4, G'_4) → poly3'_1, g'_4, k'_4, j'_4
172. Translate(I, u_1) → I'_4
173. Translate(J, u_1) → J'_5
174. Translate(G, u_1) → G'_5
175. Polygon(I'_4, J'_5, G'_5) → poly2'_1, g'_5, i'_4, j'_5
176. Translate(I'_2, u_1) → A_3
177. Translate(J'_3, u_1) → B_3
178. Translate(G'_2, u_1) → C_3
179. Polygon(A_3, B_3, C_3) → poly2''_1, c_4, a_4, b_5
180. Translate(K'_2, u_1) → D_3
181. Translate(J'_2, u_1) → E_3
182. Translate(G'_1, u_1) → F_3
183. Polygon(D_3, E_3, F_3) → poly3''_1, f_4, d_4, e_3
184. Translate(I, u_1) → I'_5
185. Translate(B, u_1) → B'_1
186. Translate(G, u_1) → G'_6
187. Polygon(I'_5, B'_1, G'_6) → poly4'_1, g'_6, i'_5, b'_1
188. Translate(M_1, v) → G_3
189. Translate(N_1, v) → H_3
190. Translate(O_1, v) → I_3
191. Polygon(G_3, H_3, I_3) → poly8, i_6, g_7, h_3
192. Translate(I_1, v) → J_3
193. Translate(J_1, v) → K_3
194. Translate(K_1, v) → L_3
195. Polygon(J_3, K_3, L_3) → poly9, l_4, j_6, k_5
196. Translate(Z', v) → Z''_1
197. Translate(B''', v) → M_3
198. Translate(L_1, v) → N_3
199. Polygon(Z''_1, M_3, N_3) → poly10, n_4, z''_1, m_4
200. Translate(K, v) → K'_5
201. Translate(J, v) → J'_6
202. Translate(G, v) → G'_7
203. Polygon(K'_5, J'_6, G'_7) → poly3'_2, g'_7, k'_5, j'_6
204. Translate(I, v) → I'_6
205. Translate(J, v) → J'_7
206. Translate(G, v) → G'_8
207. Polygon(I'_6, J'_7, G'_8) → poly2'_2, g'_8, i'_6, j'_7
208. Translate(I, v) → I'_7
209. Translate(B, v) → B'_2
210. Translate(G, v) → G'_9
211. Polygon(I'_7, B'_2, G'_9) → poly4'_2, g'_9, i'_7, b'_2
212. Translate(I'_3, v) → O_3
213. Translate(B', v) → B''_2
214. Translate(G'_3, v) → P_3
215. Polygon(O_3, B''_2, P_3) → poly4''_2, p_3, o_3, b''_2
216. Translate(I'_2, v) → Q_3
217. Translate(J'_3, v) → R_3
218. Translate(G'_2, v) → S_3
219. Polygon(Q_3, R_3, S_3) → poly2''_2, s_4, q_3, r_4
220. Translate(K'_2, v) → T_3
221. Translate(J'_2, v) → U_3
222. Translate(G'_1, v) → V_3
223. Polygon(T_3, U_3, V_3) → poly3''_2, v_4, t_4, u_4
224. Translate(M_1, w_1) → W_3
225. Translate(N_1, w_1) → Z_3
226. Translate(O_1, w_1) → A_4
227. Polygon(W_3, Z_3, A_4) → poly11, a_5, w_4, z_4
228. Translate(I_1, w_1) → B_4
229. Translate(J_1, w_1) → C_4
230. Translate(K_1, w_1) → D_4
231. Polygon(B_4, C_4, D_4) → poly12, d_5, b_6, c_5
232. Translate(Z', w_1) → Z''_2
233. Translate(B''', w_1) → E_4
234. Translate(L_1, w_1) → F_4
235. Polygon(Z''_2, E_4, F_4) → poly13, f_5, z''_2, e_4
236. Translate(I'_3, w_1) → G_4
237. Translate(B', w_1) → B''_3
238. Translate(G'_3, w_1) → H_4
239. Polygon(G_4, B''_3, H_4) → poly4''_3, h_4, g_8, b''_3
240. Translate(K, w_1) → K'_6
241. Translate(J, w_1) → J'_8
242. Translate(G, w_1) → G'_{10}
243. Polygon(K'_6, J'_8, G'_{10}) → poly3'_3, g'_{10}, k'_6, j'_8
244. Translate(I, w_1) → I'_8
245. Translate(J, w_1) → J'_9
246. Translate(G, w_1) → G'_{11}
247. Polygon(I'_8, J'_9, G'_{11}) → poly2'_3, g'_{11}, i'_8, j'_9
248. Translate(I'_2, w_1) → I_4
249. Translate(J'_3, w_1) → J_4
250. Translate(G'_2, w_1) → K_4
251. Polygon(I_4, J_4, K_4) → poly2''_3, k_6, i_7, j_7
252. Translate(K'_2, w_1) → L_4
253. Translate(J'_2, w_1) → M_4
254. Translate(G'_1, w_1) → N_4
255. Polygon(L_4, M_4, N_4) → poly3''_3, n_5, l_5, m_5
256. Translate(I, w_1) → I'_9
257. Translate(B, w_1) → B'_3
258. Translate(G, w_1) → G'_{12}
259. Polygon(I'_9, B'_3, G'_{12}) → poly4'_3, g'_{12}, i'_9, b'_3
260. Intersect(k_1, r) → O_4
261. Intersect(n_1, j_1) → P_4
262. Intersect(k_1, s) → Q_4
263. Intersect(n_1, t) → R_4
264. Intersect(c, r_1) → S_4, T_4
265. Line(P_4, B) → p_4
266. Intersect(g_1, p_4) → U_4