积极 AI Logo 积极 AI

圆内接角定理演示

圆内接角定理演示
几何画板及绘图内容加载中，请稍等……
2015-11-09 04:42
圆角几何作图
①本范例演示圆内接角定理：若两个内接角截取同一弧，则它们相等。②涉及核心概念：圆、内接角、圆心角、弧。③作图要点：使用 GeoGebra 命令 Circle（画圆）、Point（点）、CircleArc（圆弧）、Segment（线段）、Intersect（交点）、CircleSector（扇形）、Dilate（缩放）、Vector（向量）、Translate（平移）、Line（直线）、Angle（角度）、Rotate（旋转）；对象包括点 A, B, C, D, O, P 等。④适合高中数学教学，用于直观理解圆内接角定理及其应用。

GeoGebra 命令及参数

  1. Circle(A, B) → c
  2. Point(c) → C
  3. Point(c) → D
  4. CircleArc(A, C, D) → d
  5. CircleArc(A, D, C) → e
  6. Point(e) → E
  7. Point(e) → F
  8. Point(e) → J
  9. Point(e) → K
  10. Point(e) → M
  11. Segment(E, C) → a
  12. Segment(E, D) → b
  13. Segment(F, C) → f
  14. Segment(F, D) → g
  15. Segment(J, C) → n
  16. Segment(J, D) → p
  17. Segment(K, C) → q
  18. Segment(K, D) → r
  19. Segment(M, C) → a_1
  20. Segment(M, D) → b_1
  21. Circle(E, 1.5) → e_1
  22. Circle(F, 1.5) → f_1
  23. Circle(J, 1.5) → p_1
  24. Circle(K, 1.5) → q_1
  25. Circle(M, 1.5) → s_1
  26. Intersect(e_1, a, 1) → O
  27. Intersect(e_1, b, 1) → P
  28. Intersect(f_1, f, 1) → Q
  29. Intersect(f_1, g, 1) → R
  30. Intersect(p_1, n, 1) → A_1
  31. Intersect(p_1, p, 1) → B_1
  32. Intersect(q_1, q, 1) → C_1
  33. Intersect(q_1, r, 1) → D_1
  34. Intersect(s_1, a_1, 1) → G_1
  35. Intersect(s_1, b_1, 1) → H_1
  36. CircleSector(E, O, P) → c_2
  37. CircleSector(F, Q, R) → d_2
  38. CircleSector(J, A_1, B_1) → h_2
  39. CircleSector(K, C_1, D_1) → k_2
  40. CircleSector(M, G_1, H_1) → q_2
  41. Dilate(E, If[0 < o < 1, 1 - o, 0], F) → E'
  42. Vector(E, E') → u
  43. Translate(c_2, u) → s_2
  44. Line(E, g) → i_1
  45. Line(R, b) → j_1
  46. Line(F, j_1) → l_1
  47. Intersect(f_1, l_1, 2) → K_1
  48. Angle(R, F, K_1) → α
  49. Vector(F, J) → v
  50. Dilate(F, If[1.5 < o < 2.5, 2.5 - o, 0], J) → F'
  51. Vector(F, F') → w
  52. Translate(d_2, w) → h
  53. Angle(O, E, P) → β
  54. Angle(Q, F, R) → γ
  55. Line(J, g) → i
  56. Intersect(p_1, i, 2) → G
  57. Angle(B_1, J, G) → δ
  58. Angle(A_1, J, B_1) → ε
  59. Dilate(J, If[3 < o < 4, 4 - o, 0], K) → J'
  60. Vector(J, J') → j
  61. Translate(h_2, j) → k
  62. Line(K, p) → l
  63. Intersect(q_1, l) → H, I
  64. Angle(D_1, K, I) → ζ
  65. Angle(C_1, K, D_1) → η
  66. Dilate(K, If[4.5 < o < 5.5, 5.5 - o, 0], M) → K'
  67. Vector(K, K') → m
  68. Translate(k_2, m) → s
  69. Line(M, r) → t
  70. Intersect(s_1, t) → L, N
  71. Angle(H_1, M, N) → θ
  72. Angle(G_1, M, H_1) → ι
  73. Rotate(s_2, If[0 < o < 1, (o * (-α)), 0], E') → t_2
  74. Rotate(h, If[1.5 < o < 2.5, ((o - 1.5) * (-δ)), 0], F') → h'
  75. Rotate(k, If[3 < o < 4, ((o - 3) * (-ζ)), 0], J') → k'
  76. Rotate(s, If[4.5 < o < 5.5, ((o - 4.5) * (-θ)), 0], K') → s'