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Animation Demonstrating Polygon and Circle Relationships

Animation Demonstrating Polygon and Circle Relationships
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2017-05-02 23:23
CirclePolygonGeometric Construction
This example demonstrates the construction and properties of circumcircles and incircles of polygons through animation. It involves core mathematical concepts like circumcircle, incircle, polygon, angle, vector, etc. Key GeoGebra commands and objects used include Rotate, Circle, Intersect, Polygon, etc., as listed in the construction summary. Suitable for high school and above students to understand geometric relationships between polygons and circles, as well as animation techniques.

GeoGebra Commands & Parameters

  1. Rotate(B_2, (a * π / 180), A) → B'
  2. Ray(A, B') → g
  3. Point(g) → B
  4. Segment(A, B) → j
  5. Ray(A, B_2) → f
  6. Point(f) → C
  7. Segment(B, C) → h
  8. Segment(A, C) → i
  9. Min({i, j, h}) → b
  10. Angle(B_2, A, B') → α
  11. Circle(C, (0.2 * b)) → d
  12. Circle(B, 4) → c
  13. Intersect(c, g, 2) → E_2
  14. Intersect(d, f, 2) → F_2
  15. Ray(C, F_2) → k
  16. Ray(B, E_2) → l
  17. Circle(B, (0.2 * b)) → e
  18. Circle(C, (0.15 * b)) → p
  19. Angle(F_2, C, B) → β
  20. Angle(C, B, E_2) → γ
  21. Rotate(F_2, β / 2, C) → F'
  22. Angle(F_2, C, F') → δ
  23. Rotate(C, γ / 2, B) → D'
  24. Angle(C, B, D') → ε
  25. Ray(B, D') → m
  26. Ray(C, F') → n
  27. Intersect(e, m, 1) → G_2
  28. Intersect(e, h, 1) → H_2
  29. Intersect(p, h, 1) → I
  30. Polygon(A, C, B) → poly1, c_2, a_1, d_2
  31. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], C) → A'
  32. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], B) → A'_1
  33. Segment(A, A') → k_1
  34. Segment(A, A'_1) → l_1
  35. Min(c_2, d_2) → w
  36. Circle(A, (0.15 * w)) → e_2
  37. Segment(A, B) → m_2
  38. Intersect(e_2, m_2) → S,
  39. Segment(A, C) → n_2
  40. Intersect(e_2, n_2) → T,
  41. Min({h, k_1, l_1}) → b_1
  42. Intersect(d, h, 1) → U
  43. Intersect(e, h) → W,
  44. Angle(A, B, C) → λ
  45. Angle(B, C, A) → κ
  46. Rotate(A, λ / 2, B) → A'_2
  47. Angle(A, B, A'_2) → ι
  48. Ray(B, A'_2) → t_1
  49. Rotate(B, κ / 2, C) → C'_1
  50. Angle(B, C, C'_1) → μ_1
  51. Ray(C, C'_1) → f_2
  52. Intersect(d, f_2) → A_1,
  53. CircleSector(C, U, A_1) → r_2
  54. Intersect(t_1, f_2) → O
  55. OrthogonalLine(O, k_1) → s_2
  56. OrthogonalLine(O, l_1) → t_2
  57. Intersect(s_2, k_1) → E
  58. Intersect(t_2, l_1) → F
  59. Intersect(k_1, t_1) → D_1
  60. Circle(A, (0.2 * b)) → q_2
  61. Angle(C, A, B) → μ
  62. Rotate(C, μ / 2, A) → D'_2
  63. Angle(C, A, D'_2) → ν
  64. Ray(A, D'_2) → a_2
  65. Intersect(q_2, a_2) → V,
  66. Intersect(q_2, k_1) → E_1,
  67. CircleSector(A, E_1, V) → p_2
  68. Dilate(C, If[1 < o ≤ 2, 2 - o, 0], O) → D'_3
  69. Dilate(A, If[1 < o ≤ 2, 2 - o, 0], O) → A'_3
  70. Segment(A, A'_3) → b_2
  71. Segment(C, D'_3) → f_3
  72. Rotate(r_2, If[2.5 < o ≤ 3.5, ((o - 2.5) * κ / 2), κ / 2], C) → c_3
  73. Rotate(p_2, If[3.5 < o ≤ 4.5, ((o - 3.5) * μ / 2), μ / 2], A) → d_3
  74. Dilate(O, If[5 < o ≤ 6, 6 - o, 0], F) → Z'
  75. Dilate(O, If[5 < o ≤ 6, 6 - o, 0], E) → Z'_1
  76. Segment(O, Z') → g_3
  77. Segment(O, Z'_1) → h_3
  78. Angle(O, E, A) → ξ
  79. Angle(A, F, O) → ο
  80. Circle(O, Z') → e_3
  81. Rotate(F, If[6 < o ≤ 9, (((o - 6) * 2) * π / 3), (2 * π)], O) → F_1
  82. Segment(B, D_1) → i_3
  83. Intersect(e, i_3) → G_1,
  84. Intersect(e, l_1) → H_1,
  85. Dilate(B, If[9.5 < o ≤ 10.5, 10.5 - o, 0], O) → C'_2
  86. Polygon(A, O, B) → poly2, c_4, a_3, z_1
  87. CircleArc(O, Z', F_1) → k_3
  88. OrthogonalLine(O, h) → q
  89. Intersect(q, h) → D
  90. Line(A, O) → r
  91. Line(F, D) → s
  92. Intersect(r, s) → H
  93. Line(C, O) → t
  94. Intersect(s, t) → G
  95. Dilate(O, If[5 < o ≤ 6, 6 - o, 0], D) → O'
  96. Segment(O, O') → f_1
  97. Angle(O, D, C) → ζ
  98. Circle(A, G, F) → c_1
  99. Circle(C, H, D) → d_1
  100. Ray(D, H) → g_1
  101. Ray(F, G) → h_1
  102. Dilate(F, If[9 < o ≤ 10, 10 - o, 0], D) → F'_1
  103. Segment(F, F'_1) → i_1
  104. Dilate(O, If[10 < o ≤ 11, 11 - o, 0], H) → O'_1
  105. Segment(O, O'_1) → j_1
  106. Dilate(O, If[10 < o ≤ 11, 11 - o, 0], G) → O'_2
  107. Segment(O, O'_2) → m_1
  108. Center(c_1) → J
  109. Rotate(F, If[11 < o ≤ 13, ((o - 11) * π), (2 * π)], J) → F'_2
  110. CircleArc(J, F, F'_2) → e_1
  111. Center(d_1) → K
  112. Rotate(D, If[13 < o ≤ 15, ((o - 13) * π), (2 * π)], K) → D'_1
  113. CircleArc(K, D, D'_1) → p_1
  114. Dilate(E, If[15 < o ≤ 16, 16 - o, 0], H) → F'_3
  115. Dilate(E, If[15 < o ≤ 16, 16 - o, 0], G) → E'
  116. Segment(E, F'_3) → n_1
  117. Segment(E, J) → q_1
  118. Segment(E, E') → r_1
  119. Angle(G, H, E) → τ
  120. Angle(H, G, E) → θ
  121. Line(A, h_1) → s_1
  122. Intersect(d_1, s_1, 1) → L
  123. Line(B, A) → g_2
  124. Point(g_2) → M
  125. Polygon(E, H, G) → poly3, g_4, e_4, h_2
  126. Angle(L, A, B) → ρ
  127. Dilate(A, If[16 < o ≤ 17, 17 - o, 0], G) → A'_4
  128. Vector(A, A'_4) → u
  129. Translate(d_3, u) → k_2
  130. Rotate(k_2, If[17 < o ≤ 18, ((-(o - 17)) * ρ), (-ρ)], G) → p_3
  131. Midpoint(A, G) → N
  132. Dilate(A, If[18 < o ≤ 19, 19 - o, 0], N) → A'_5
  133. Vector(A, A'_5) → v
  134. Translate(d_3, v) → q_3
  135. Rotate(q_3, If[19 < o ≤ 20, ((-(o - 19)) * (ρ + θ / 2)), (-(ρ + θ / 2))], N) → r_3
  136. Dilate(N, If[20 < o ≤ 21, 21 - o, 0], G) → N'
  137. Vector(N, N') → u_1
  138. Translate(r_3, u_1) → s_3
  139. Line(C, g_1) → i_2
  140. Intersect(d_1, i_2, 2) → P
  141. Midpoint(C, H) → Q
  142. Angle(O, C, P) → σ
  143. Dilate(C, If[21 < o ≤ 22, 22 - o, 0], H) → C'
  144. Vector(C, C') → v_1
  145. Translate(c_3, v_1) → t_3
  146. Rotate(t_3, If[22 < o ≤ 23, ((o - 22) * σ), σ], H) → d_4
  147. Dilate(C, If[23 < o ≤ 24, 24 - o, 0], Q) → C'_3
  148. Vector(C, C'_3) → w_1
  149. Translate(c_3, w_1) → f_4
  150. Rotate(f_4, If[24 < o ≤ 25, ((o - 24) * (σ + τ / 2)), σ + τ / 2], Q) → h_4
  151. Dilate(Q, If[25 < o ≤ 26, 26 - o, 0], H) → Q'
  152. Vector(Q, Q') → u_2
  153. Translate(h_4, u_2) → k_4
  154. Circle(A, G, H) → p_4
  155. Center(p_4) → R
  156. Rotate(H, If[26 < o ≤ 28, ((o - 26) * π), (2 * π)], R) → H'
  157. CircleArc(R, H, H') → q_4
  158. Distance(A, R) → distanceAR
  159. Distance(R, C) → distanceRC