开放中题:圆内接四边形作图练习

开放中题:圆内接四边形作图练习
几何画板及绘图内容加载中,请稍等……
2023-05-18 21:38
本范例演示如何利用圆内接四边形的性质进行几何作图。核心数学概念包括圆内接四边形、角度关系、旋转与坐标变换。作图要点涉及使用GeoGebra命令如Polygon、Rotate、Circle等对象进行构造。适合初中或高中几何学习者,用于理解四边形与圆的关联及动态几何应用。

GeoGebra 命令及参数

  1. Polygon(A0, B, 4) → poly0, f, g, h, i, A, C
  2. Polygon(A3, H, 4) → poly3, j, k, l, m, E, G
  3. Polygon(A7, P, 4) → poly7, n, p, q, r, I, K
  4. Polygon(A1, D, 4) → poly1, s, t, a, b, M, O
  5. Polygon(A6, N, 4) → poly6, c, d, e, f_1, Q, S
  6. Polygon(A2, H2, 4) → poly2, k_1, l_1, m_1, n_1, W, Z
  7. Polygon(A8, A8 + (2, 0), 4) → poly8, g_1, h_1, i_1, j_1, U, V
  8. Polygon(A9, T, 4) → poly9, p_1, q_1, r_1, s_1, A_1, B_1
  9. Polygon(A4, J, 4) → poly4, t_1, a_1, b_1, c_1, C_1, D_1
  10. Polygon(A5, L, 4) → poly5, d_1, e_1, f_2, g_2, E_1, F_1
  11. Polygon(K_1, L_1, 4) → poly10, l_2, m_2, n_2, p_2, M_1, N_1
  12. Polygon(O_1, P_1, 4) → poly12, q_2, r_2, s_2, t_2, Q_1, R_1
  13. Polygon(S_1, T_1, 4) → poly13, a_2, b_2, c_2, d_2, U_1, V_1
  14. Polygon(C_2, D_2, 4) → poly15, i_3, j_3, k_3, l_3, E_2, F_2
  15. Polygon(G_2, H_2, 4) → poly16, m_3, n_3, p_3, q_3, I_2, J_2
  16. Polygon(G_{3}, H_{3}, 4) → poly17, m_{4}, n_{4}, p_{4}, q_{4}, I_{3}, J_{3}
  17. Polygon(C_{3}, D_{3}, 4) → poly14, i_{4}, j_{4}, k_{4}, l_{4}, E_{3}, F_{3}
  18. If(aleft > aright, "Left side is bigger.", aleft < aright, "Right side is bigger", "Both sides are equal!") → text9
  19. nCr(4, 2) → w
  20. If(o_1 ≟ 0, p15 / p10, ((-p15)) / p10) → u_2
  21. If(u_1 ≟ 0, p12 / p13, ((-p12)) / p13) → v_2
  22. If(w_1 ≟ 0, p17 / p14, ((-p17)) / p14) → w_2
  23. If(o_2 ≟ 0, p16, (-p16)) → b_3
  24. Polygon(T_2, U_2, 4) → poly11, s_3, t_3, a_3, c_3, V_2, W_2
  25. Polygon(Z_2, A_3, 4) → poly18, d_3, e_3, f_4, g_4, B_3, M_3
  26. Circle(N_3, O_3) → c_4
  27. Point(c_4) → P_3
  28. Point(c_4) → Q_3
  29. Point(c_4) → R_3
  30. Point(c_4) → S_3
  31. Polygon(S_3, P_3, Q_3, R_3) → q1, h_4, r_4, s_4, t_4
  32. Segment(Q_3, R_3) → a_4
  33. Segment(R_3, S_3) → b_4
  34. Segment(S_3, P_3) → d_4
  35. Segment(P_3, Q_3) → e_4
  36. Circle(A_2, B_2) → e_2
  37. Point(e_2) → O_2
  38. Point(e_2) → P_2
  39. Segment(O_2, P_2) → h_2
  40. Rotate(P_2, (((100 * p13) + (10 * p12) + p16) * pi / 180), O_2) → R_2
  41. Ray(O_2, R_2) → i_2
  42. Intersect(e_2, i_2, 2) → S_2
  43. Rotate(O_2, ((-((10 * p14) + p18)) * pi / 180), P_2) → T_3
  44. Ray(P_2, T_3) → j_2
  45. Intersect(e_2, j_2, 2) → U_3
  46. Segment(O_2, S_2) → k_2
  47. Segment(P_2, U_3) → f_3
  48. Rotate(P_2, ((-((10 * p11) + p17)) * pi / 180), U_3) → V_3
  49. Ray(U_3, V_3) → g_3
  50. Intersect(e_2, g_3, 2) → W_3
  51. Angle(P_2, O_2, S_2) → α
  52. Angle(U_3, P_2, O_2) → β
  53. Angle(W_3, U_3, P_2) → γ
  54. Segment(U_3, W_3) → h_3
  55. Rotate(O_2, (((10 * p15) + p10) * pi / 180), S_2) → Z_3
  56. Ray(S_2, Z_3) → r_3
  57. Intersect(e_2, r_3, 2) → A_4
  58. Angle(A_4, S_2, O_2) → δ
  59. Segment(S_2, A_4) → f_5

AI 绘图提示语参考

绘制一个动态的圆内接四边形探究图。先画一个大圆,在圆上取四个点,依次连接构成一个四边形。然后,以四边形各边为边,向外或向内构造多个正方形,这些正方形围绕圆排列。接着,在圆外再画一个辅助圆,并在其上取点,构造旋转射线,形成角度关系。最后,添加文本比较左右两侧的数值大小,并显示组合数计算结果。整体图形展示圆与多边形、角度变换及面积比较的几何关系。
以上提示语为根据原始绘图命令整理而来,仅供参考。