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圆中三弦共点的特殊定理动态演示

圆中三弦共点的特殊定理动态演示
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2016-12-03 09:24
圆角几何作图
所属专题 Circles (Theorems)
该范例动态展示了圆中一组特殊共点弦的几何性质。核心数学概念包括圆、角度和几何作图。通过使用GeoGebra命令如Circle、Point、Rotate、Intersect等，可以直观地观察到这些弦的性质。适合高中数学教学和学习。

GeoGebra 命令及参数

  1. Circle(A, B) → c
  2. Radius(c) → o
  3. Point(c) → D
  4. Point(c) → C
  5. Segment(C, D) → f
  6. Point(f) → E
  7. Rotate(C, π / 3, E) → C'
  8. Line(E, C') → g
  9. Intersect(c, g, 2) → F
  10. Line(F, g_1) → l_1
  11. Point(l_1) → G_1
  12. Angle(C, E, C') → α
  13. Rotate(C', π / 3, E) → C''
  14. Angle(C', E, C'') → β
  15. Line(E, C'') → h
  16. Segment(C, E) → i
  17. Segment(E, D) → j
  18. Intersect(c, g, 1) → G
  19. Segment(E, F) → k
  20. Segment(E, G) → l
  21. Intersect(c, h, 1) → H
  22. Intersect(c, h, 2) → I
  23. Segment(E, H) → m
  24. Segment(E, I) → n
  25. Min(list) → a
  26. Circle(E, (0.28 * a)) → d
  27. Intersect(d, k, 1) → J
  28. Intersect(f, i) → K
  29. Intersect(f, i) → L
  30. Intersect(f, i) → M
  31. Intersect(f, i) → N
  32. Intersect(d, i) → O,
  33. Intersect(d, m) → P, H_1
  34. CircleSector(E, P, O) → e
  35. Segment(D, E) → p
  36. Segment(E, C) → q
  37. Dilate(I, If[0 < b ≤ 1, 1 - b, 0], E) → I'
  38. Segment(I, I') → r
  39. Intersect(c, r, 1) → R
  40. Dilate(E, If[1 < b ≤ 2, 2 - b, 0], H) → E'
  41. Segment(E, E') → s
  42. Dilate(F, If[2 < b ≤ 3, 3 - b, 0], E) → F'
  43. Segment(F, F') → t
  44. Dilate(E, If[3 < b ≤ 4, 4 - b, 0], G) → E'_1
  45. Segment(E, E'_1) → f_1
  46. Rotate(e, If[5 < b ≤ 6, ((b - 5) * π / 3), π / 3], E) → e'
  47. Rotate(e', If[7 < b ≤ 8, ((b - 7) * π / 3), π / 3], E) → e''
  48. Circle(Q, p) → c_1
  49. Intersect(c_1, g_1, 2) → T
  50. Circle(T, t) → d_1
  51. Intersect(d_1, g_1, 2) → U
  52. Circle(U, s) → e_1
  53. Intersect(e_1, g_1, 2) → V
  54. Circle(S, r) → k_1
  55. Line(E, g_1) → i_1
  56. Line(D, g_1) → j_1
  57. Dilate(S, If[9 < b ≤ 10, 10 - b, 0], Q) → S'
  58. Segment(S, S') → m_1
  59. Dilate(Q, If[10 < b ≤ 11, 11 - b, 0], V) → Q'
  60. Vector(Q, Q') → w
  61. Translate(S, w) → S'_1
  62. Translate(S', w) → S''
  63. Segment(S'_1, S'') → n_1
  64. Point(j_1) → B_1
  65. Point(j_1) → C_1
  66. Angle(B_1, D, E) → γ
  67. Dilate(D, If[11 < b ≤ 12, 12 - b, 0], Q) → D'
  68. Vector(D, D') → u_1
  69. Translate(D, u_1) → D'_1
  70. Translate(E, u_1) → E'_2
  71. Segment(D'_1, E'_2) → p'
  72. Rotate(D'_1, If[11 < b ≤ 12, ((-(b - 11)) * γ), (-γ)], D'_1) → D_1
  73. Rotate(E'_2, If[11 < b ≤ 12, ((-(b - 11)) * γ), (-γ)], D'_1) → E_1
  74. Segment(D_1, E_1) → p''
  75. Dilate(F, If[12 < b ≤ 13, 13 - b, 0], T) → F'_1
  76. Vector(F, F'_1) → v_1
  77. Translate(F, v_1) → F'_2
  78. Translate(F', v_1) → F''
  79. Angle(E, F, G_1) → δ
  80. Segment(F'_2, F'') → t'
  81. Rotate(F'_2, If[12 < b ≤ 13, ((b - 12) * δ), δ], F'_1) → F_1
  82. Rotate(F'', If[12 < b ≤ 13, ((b - 12) * δ), δ], F'_1) → F'''
  83. Segment(F_1, F''') → t''
  84. Line(H, j_1) → r_1
  85. Point(r_1) → I_1
  86. Dilate(H, If[13 < b ≤ 14, 14 - b, 0], U) → H'
  87. Angle(I_1, H, E) → ε
  88. Vector(H, H') → w_1
  89. Translate(E, w_1) → E'_3
  90. Translate(E', w_1) → E''
  91. Segment(E'_3, E'') → s'
  92. Rotate(E'_3, If[13 < b ≤ 14, ((-(b - 13)) * ε), (-ε)], E'') → J_1
  93. Rotate(E'', If[13 < b ≤ 14, ((-(b - 13)) * ε), (-ε)], E'') → E'''
  94. Segment(J_1, E''') → s''
  95. Dilate(G, If[14 < b ≤ 15, 15 - b, 0], S) → G'
  96. Vector(G, G') → a_1
  97. Translate(E, a_1) → E'_4
  98. Translate(E'_1, a_1) → K_1
  99. Segment(E'_4, K_1) → s_1
  100. Line(G, j_1) → t_1
  101. Point(t_1) → L_1
  102. Angle(L_1, G, E) → ζ
  103. Rotate(E'_4, If[14 < b ≤ 15, ((-(b - 14)) * ζ), (-ζ)], K_1) → M_1
  104. Rotate(K_1, If[14 < b ≤ 15, ((-(b - 14)) * ζ), (-ζ)], K_1) → N_1
  105. Segment(M_1, N_1) → b_1
  106. Circle(S, b_1) → c_2
  107. Intersect(c_2, h_1, 2) → O_1
  108. Circle(O_1, r) → p_1
  109. Intersect(p_1, h_1, 2) → W
  110. Dilate(R, If[15 < b ≤ 16, 16 - b, 0], O_1) → R'
  111. Vector(I, R') → q_1
  112. Translate(I, q_1) → I'_1
  113. Translate(I', q_1) → I''
  114. Segment(I'_1, I'') → r'
  115. Line(I, i_1) → f_2
  116. Point(f_2) → Z
  117. Angle(E, I, Z) → η
  118. Rotate(I'_1, If[15 < b ≤ 16, ((b - 15) * η), η], I'_1) → A_1
  119. Rotate(I'', If[15 < b ≤ 16, ((b - 15) * η), η], I'_1) → I'''
  120. Segment(A_1, I''') → r''
  121. Dilate(E, If[16 < b ≤ 17, 17 - b, 0], W) → E'_5
  122. Vector(E, E'_5) → u_2
  123. Translate(E, u_2) → E'_6
  124. Translate(C, u_2) → C'_1
  125. Segment(E'_6, C'_1) → q'
  126. Point(i_1) → P_1
  127. Angle(P_1, E, C) → θ
  128. Rotate(E'_6, If[16 < b ≤ 17, ((-(b - 16)) * θ), (-θ)], E'_6) → Q_1
  129. Rotate(C'_1, If[16 < b ≤ 17, ((-(b - 16)) * θ), (-θ)], E'_6) → R_1
  130. Segment(Q_1, R_1) → q''
  131. Dilate(G, If[17 < b ≤ 18, 18 - b, 0], E) → G'_1
  132. Dilate(D, If[17 < b ≤ 18, 18 - b, 0], E) → D'_2
  133. Dilate(R, If[17 < b ≤ 18, 18 - b, 0], E) → R'_1
  134. Dilate(F, If[17 < b ≤ 18, 18 - b, 0], E) → F'_3
  135. Dilate(C, If[17 < b ≤ 18, 18 - b, 0], E) → C'_2
  136. Dilate(H, If[17 < b ≤ 18, 18 - b, 0], E) → H'_1
  137. Segment(D, D'_2) → g_2
  138. Segment(I, R'_1) → h_2
  139. Segment(F, F'_3) → i_2
  140. Segment(C, C'_2) → j_2
  141. Segment(H, H'_1) → k_2
  142. Segment(G, G'_1) → l_2