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Inscribed Angle Action! (2 Theorems)

Inscribed Angle Action! (2 Theorems)
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2016-01-18 23:59
CircleAngleGeometric Construction
This example demonstrates two theorems related to inscribed angles. Key mathematical concepts include circles, angles, and inscribed angles. Using GeoGebra commands such as Circle, Segment, Point, etc., it dynamically illustrates the properties of inscribed angles. Suitable for middle school and above students to learn geometric construction and circle theorems.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Segment(B, A) → a
  3. Point(c) → C
  4. Segment(A, C) → b
  5. Point(c) → D
  6. CircumcircleArc(C, D, B) → d
  7. CircleArc(A, B, C) → e
  8. Point(d) → E
  9. Segment(C, E) → f
  10. Segment(E, B) → g
  11. Circle(E, 1.5) → h
  12. Ray(E, C) → i
  13. Ray(E, B) → j
  14. Intersect(h, j) → F,
  15. Intersect(h, i) → G,
  16. CircleSector(E, F, G) → k
  17. Segment(E, A) → l
  18. Line(A, xAxis) → m
  19. Dilate(E, If[0 ≤ n ≤ 1, 1 - n, 0], A) → E'
  20. Vector(E, E') → u
  21. Translate(k, u) → k'
  22. Line(E, a) → p
  23. Line(E, b) → q
  24. Intersect(h, p, 1) → H
  25. Angle(H, E, B) → α
  26. Intersect(h, q, 2) → I
  27. Angle(C, E, I) → β
  28. Dilate(E, If[1 < n ≤ 2, 2 - n, 0], A) → E'_1
  29. Vector(E, E'_1) → v
  30. Translate(k, v) → k'_1
  31. Rotate(k'_1, If[1 < n ≤ 2, ((n - 1) * β), β], E'_1) → k''
  32. Rotate(k', If[0 < n ≤ 1, ((-n) * α), (-α)], E') → k''_1
  33. Circle(A, 1.5) → r
  34. Intersect(r, a, 1) → J
  35. Intersect(r, b, 1) → K
  36. CircleSector(A, J, K) → s
  37. Point(d) → L
  38. Point(d) → M
  39. Point(d) → N
  40. Point(d) → O
  41. Point(d) → P
  42. Segment(L, B) → t
  43. Segment(L, C) → a_1
  44. Segment(M, B) → b_1
  45. Segment(M, C) → c_1
  46. Segment(N, B) → d_1
  47. Segment(N, C) → e_1
  48. Segment(O, B) → f_1
  49. Segment(O, C) → g_1
  50. Segment(P, C) → h_1
  51. Segment(P, B) → i_1
  52. Vector(E, L) → w_2
  53. Vector(E, P) → j_1
  54. Circle(L, 1.5) → k_1
  55. Circle(M, 1.5) → p_1
  56. Circle(N, 1.5) → q_1
  57. Circle(O, 1.5) → r_1
  58. Circle(P, 1.5) → s_1
  59. Intersect(k_1, t, 1) → Q
  60. Intersect(k_1, a_1, 1) → R
  61. Intersect(p_1, b_1, 1) → S
  62. Intersect(p_1, c_1, 1) → T
  63. Intersect(q_1, d_1) → U,
  64. Intersect(q_1, e_1, 1) → V
  65. Intersect(r_1, f_1, 1) → W
  66. Intersect(r_1, g_1, 1) → Z
  67. Intersect(s_1, i_1, 1) → A_1
  68. Intersect(s_1, h_1, 1) → B_1
  69. CircleSector(M, S, T) → t_1
  70. CircleSector(L, Q, R) → c_2
  71. CircleSector(N, U, V) → d_2
  72. CircleSector(O, W, Z) → e_2
  73. CircleSector(P, A_1, B_1) → f_2
  74. Dilate(E, If[0 < w < 1, 1 - w, 0], L) → E'_2
  75. Vector(E, E'_2) → l_1
  76. Translate(k, l_1) → k'_2
  77. Line(E, a_1) → m_1
  78. Point(m_1) → C_1
  79. Angle(C, E, C_1) → γ
  80. Rotate(k'_2, If[0 < w < 1, (w * γ), 0], E'_2) → g_2
  81. Dilate(L, If[1 < w < 2, 2 - w, 0], O) → L'
  82. Vector(L, L') → u_1
  83. Line(L, f_1) → n_1
  84. Translate(c_2, u_1) → h_2
  85. Intersect(k_1, n_1, 2) → D_1
  86. Angle(D_1, L, Q) → δ
  87. Rotate(h_2, If[1 < w < 2, ((-(w - 1)) * δ), 0], L') → k_2
  88. Dilate(O, If[2 < w < 3, 3 - w, 0], M) → O'
  89. Vector(O, O') → w_1
  90. Translate(e_2, w_1) → p_2
  91. Line(O, c_1) → a_2
  92. Intersect(r_1, a_2, 2) → E_1
  93. Angle(Z, O, E_1) → ε
  94. Rotate(p_2, If[2 < w < 3, ((w - 2) * ε), 0], O') → q_2
  95. Dilate(M, If[3 < w < 4, 4 - w, 0], P) → M'
  96. Vector(M, M') → v_1
  97. Translate(t_1, v_1) → r_2
  98. Line(M, i_1) → b_2
  99. Intersect(p_1, b_2, 2) → F_1
  100. Angle(S, M, F_1) → ζ
  101. Rotate(r_2, If[3 < w < 4, ((w - 3) * ζ), 0], M') → s_2
  102. Dilate(P, If[4 < w < 5, 5 - w, 0], N) → P'
  103. Vector(P, P') → u_2
  104. Translate(f_2, u_2) → t_2
  105. Line(P, e_1) → i_2
  106. Intersect(s_1, i_2, 2) → G_1
  107. Angle(B_1, P, G_1) → η
  108. Rotate(t_2, If[4 < w < 5, ((w - 4) * η), 0], P') → c_3