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GoGeometry Action 113

GoGeometry Action 113
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2017-12-21 09:41
CircleFunctionGeometric Construction
This dynamic and modifiable illustration demonstrates concepts such as incircle, median value, function graph, and kite. It is based on a problem posted by Antonio Gutierrez on Twitter. The construction uses commands like Rotate, Angle, Segment, Ray, Point, Intersect, OrthogonalLine, Circle, Distance, and more. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Rotate(A, (a * π / 180), B) → A'
  2. Angle(A, B, A') → α
  3. Segment(B, A) → f
  4. Ray(B, A') → g
  5. Point(g) → C
  6. Segment(B, C) → h
  7. Segment(C, A) → i
  8. Angle(C, A, B) → β
  9. Rotate(C, β / 2, A) → C'
  10. Angle(C, A, C') → γ
  11. Ray(A, C') → j
  12. Rotate(A, α / 2, B) → A'_1
  13. Angle(A, B, A'_1) → δ
  14. Ray(B, A'_1) → k
  15. Intersect(j, k) → D
  16. OrthogonalLine(D, f) → l
  17. Intersect(l, f) → E
  18. Circle(D, E) → c
  19. Segment(B, D) → m
  20. Segment(D, A) → n
  21. Segment(C, D) → p
  22. Intersect(c, m, 1) → F
  23. Intersect(c, p, 1) → G
  24. Intersect(c, n, 1) → H
  25. OrthogonalLine(F, m) → q
  26. OrthogonalLine(G, p) → r
  27. OrthogonalLine(H, n) → s
  28. Intersect(q, f) → I
  29. Angle(F, I, B) → ε
  30. Rotate(F, ε / 2, I) → F'
  31. Angle(F, I, F') → ζ
  32. Ray(I, F') → t
  33. Intersect(m, t) → J
  34. OrthogonalLine(J, f) → b
  35. Intersect(b, f) → K
  36. Circle(J, K) → d
  37. Intersect(q, h) → L
  38. Segment(I, L) → e
  39. Intersect(f, s) → M
  40. Angle(A, M, H) → η
  41. Rotate(A, η / 2, M) → A'_2
  42. Angle(A, M, A'_2) → θ
  43. Ray(M, A'_2) → f_1
  44. Intersect(n, f_1) → N
  45. OrthogonalLine(N, f) → g_1
  46. Intersect(g_1, f) → O
  47. Circle(N, O) → c_1
  48. Intersect(s, i) → P
  49. Segment(M, P) → h_1
  50. Intersect(r, i) → Q
  51. Intersect(r, h) → R
  52. Angle(C, Q, G) → κ
  53. Rotate(C, κ / 2, Q) → C'_1
  54. Angle(C, Q, C'_1) → ι
  55. Ray(Q, C'_1) → i_1
  56. Intersect(p, i_1) → S
  57. OrthogonalLine(S, i) → j_1
  58. Intersect(j_1, i) → T
  59. Circle(S, T) → d_1
  60. Segment(R, Q) → k_1
  61. OrthogonalLine(N, i) → l_1
  62. Intersect(l_1, i) → U
  63. OrthogonalLine(S, h) → m_1
  64. Intersect(h, m_1) → V
  65. Segment(S, V) → n_1
  66. Segment(J, K) → p_1
  67. Segment(N, U) → q_1
  68. OrthogonalLine(D, f) → r_1
  69. Intersect(f, r_1) → W
  70. Circle(D, o) → e_1
  71. Intersect(e_1, r_1, 1) → Z
  72. Circle(Z, u) → s_1
  73. Intersect(s_1, r_1, 1) → A_1
  74. Distance(A_1, W) → distanceA1W
  75. Circle(B, p_1) → t_1
  76. Circle(C, n_1) → d_2
  77. Circle(A, q_1) → k_2
  78. Segment(B, C) → a_1
  79. Segment(C, A) → b_1
  80. Segment(B, A) → f_2
  81. Max({p_1 + n_1, n_1 + q_1, q_1 + p_1}) → w_1
  82. OrthogonalLine(B, f_2) → g_2
  83. OrthogonalLine(A, f_2) → h_2
  84. Circle(B, w_1 + 0.3) → c_2
  85. Circle(A, w_1 + 0.3) → e_2
  86. Intersect(c_2, g_2, 1) → B_1
  87. Intersect(e_2, h_2, 1) → C_1
  88. Line(B_1, C_1) → i_2
  89. Circle(B_1, p_1) → p_2
  90. Intersect(p_2, i_2, 2) → D_1
  91. Circle(D_1, n_1) → q_2
  92. Intersect(q_2, i_2, 2) → E_1
  93. Circle(E_1, n_1) → r_2
  94. Intersect(r_2, i_2, 2) → F_1
  95. Circle(F_1, q_1) → s_2
  96. Intersect(s_2, i_2) → G_1, H_1
  97. Circle(H_1, q_1) → t_2
  98. Intersect(t_2, i_2, 2) → I_1
  99. Circle(I_1, p_1) → c_3
  100. Intersect(c_3, i_2) → J_1, K_1
  101. Semicircle(B_1, E_1) → d_3
  102. Semicircle(E_1, H_1) → e_3
  103. Semicircle(H_1, K_1) → f_3
  104. OrthogonalLine(D_1, i_2) → j_2
  105. OrthogonalLine(F_1, i_2) → l_2
  106. OrthogonalLine(I_1, i_2) → m_2
  107. Intersect(d_3, j_2, 1) → L_1
  108. Intersect(e_3, l_2, 1) → M_1
  109. Intersect(f_3, m_2, 1) → N_1
  110. Angle(L_1, D_1, B_1) → λ
  111. Angle(M_1, F_1, E_1) → μ
  112. Angle(N_1, I_1, H_1) → ν
  113. Polygon(B, A, C) → t1, c_4, b_2, a_2
  114. Segment(D, W) → n_2
  115. Segment(B_1, D_1) → i_3
  116. Segment(D_1, E_1) → j_3
  117. Segment(E_1, F_1) → l_3
  118. Segment(F_1, H_1) → m_3
  119. Segment(H_1, I_1) → n_3
  120. Segment(I_1, K_1) → q_3
  121. Segment(K_1, C_1) → r_3
  122. Angle(I, F, D) → ξ
  123. Angle(P, H, D) → ο
  124. Angle(R, G, D) → ρ
  125. Dilate(K, If[0 < w ≤ 1, 1 - w, 0], B_1) → K'
  126. Vector(K, K') → u_1
  127. Translate(J, u_1) → J'
  128. Translate(K, u_1) → K'_1
  129. Segment(J', K'_1) → s_3
  130. Rotate(J', If[1 < w ≤ 2, ((-(w - 1)) * π / 2), ((-π)) / 2], B_1) → J''
  131. Rotate(K'_1, If[1 < w ≤ 2, ((-(w - 1)) * π / 2), ((-π)) / 2], B_1) → O_1
  132. Segment(J'', O_1) → t_3
  133. Line(V, r_3) → a_3
  134. Point(a_3) → P_1
  135. Angle(S, V, P_1) → σ
  136. Dilate(V, If[2 < w ≤ 3, 3 - w, 0], D_1) → V'
  137. Vector(V, V') → v_1
  138. Translate(S, v_1) → S'
  139. Translate(V, v_1) → V'_1
  140. Segment(S', V'_1) → b_3
  141. Rotate(S', If[3 < w ≤ 4, ((w - 3) * σ), σ], D_1) → S''
  142. Rotate(V'_1, If[3 < w ≤ 4, ((w - 3) * δ), δ], D_1) → Q_1
  143. Segment(S'', Q_1) → f_4
  144. Rotate(S'', If[4 < w ≤ 5, ((w - 4) * π), π], E_1) → S'''
  145. Rotate(Q_1, If[4 < w ≤ 5, ((w - 4) * π), π], E_1) → R_1
  146. Segment(S''', R_1) → g_4
  147. Dilate(N, If[5 < w ≤ 6, 6 - w, 0], F_1) → N'
  148. Vector(N, N') → u_2
  149. Translate(N, u_2) → N'_1
  150. Translate(U, u_2) → U'
  151. Segment(N'_1, U') → h_4
  152. Line(N, r_3) → i_4
  153. Intersect(i_4, b_1) → S_1
  154. Angle(S_1, N, U) → τ
  155. Rotate(N'_1, If[6 < w ≤ 7, ((-(w - 6)) * τ), (-τ)], F_1) → T_1
  156. Rotate(U', If[6 < w ≤ 7, ((-(w - 6)) * τ), (-τ)], F_1) → U''
  157. Segment(T_1, U'') → j_4
  158. Rotate(T_1, If[7 < w ≤ 8, ((-(w - 7)) * π), (-π)], H_1) → U_1
  159. Rotate(U'', If[7 < w ≤ 8, ((-(w - 7)) * π), (-π)], H_1) → U'''
  160. Segment(U_1, U''') → k_4
  161. Dilate(K, If[8 < w ≤ 9, 9 - w, 0], I_1) → K'_2
  162. Vector(K, K'_2) → v_2
  163. Translate(J, v_2) → J'_1
  164. Translate(K, v_2) → K'_3
  165. Segment(J'_1, K'_3) → l_4
  166. Rotate(J'_1, If[9 < w ≤ 10, ((-(w - 9)) * π / 2), ((-π)) / 2], I_1) → V_1
  167. Rotate(K'_3, If[9 < w ≤ 10, ((-(w - 9)) * π / 2), ((-π)) / 2], I_1) → W_1
  168. Segment(V_1, W_1) → m_4
  169. Midpoint(B_1, E_1) → Z_1
  170. Midpoint(E_1, H_1) → A_2
  171. Midpoint(H_1, K_1) → B_2
  172. Rotate(E_1, If[10 < w ≤ 11, ((w - 10) * π), π], Z_1) → C_2
  173. CircleArc(Z_1, E_1, C_2) → d_4
  174. Rotate(H_1, If[11 < w ≤ 12, ((w - 11) * π), π], A_2) → D_2
  175. CircleArc(A_2, H_1, D_2) → e_4
  176. Rotate(K_1, If[12 < w ≤ 13, ((w - 12) * π), π], B_2) → E_2
  177. CircleArc(B_2, K_1, E_2) → p_4
  178. Dilate(L_1, If[13 < w ≤ 14, 14 - w, 0], D_1) → F_2
  179. Dilate(M_1, If[13 < w ≤ 14, 14 - w, 0], F_1) → G_2
  180. Dilate(N_1, If[13 < w ≤ 14, 14 - w, 0], I_1) → H_2
  181. Segment(L_1, F_2) → n_4
  182. Segment(M_1, G_2) → q_4
  183. Segment(N_1, H_2) → r_4
  184. Dilate(D, If[14 < w ≤ 15, 15 - w, 0], Z) → D'
  185. Dilate(Z, If[15 < w ≤ 16, 16 - w, 0], A_1) → Z'
  186. Dilate(A_1, If[16 < w ≤ 17, 17 - w, 0], W) → I_2
  187. Segment(D, D') → s_4
  188. Segment(Z, Z') → t_4
  189. Segment(A_1, I_2) → a_4
  190. Angle(D, W, B) → υ
  191. Dilate(L_1, If[17 < w ≤ 18, 18 - w, 0], D) → J_2
  192. Dilate(M_1, If[18 < w ≤ 19, 19 - w, 0], Z) → K_2
  193. Dilate(N_1, If[19 < w ≤ 20, 20 - w, 0], A_1) → L_2
  194. Vector(L_1, J_2) → w_2
  195. Translate(L_1, w_2) → O_2
  196. Translate(F_2, w_2) → P_2
  197. Segment(O_2, P_2) → b_4
  198. Vector(M_1, K_2) → u_3
  199. Translate(M_1, u_3) → M_2
  200. Translate(G_2, u_3) → N_2
  201. Segment(M_2, N_2) → f_5
  202. Vector(N_1, L_2) → v_3
  203. Translate(N_1, v_3) → Q_2
  204. Translate(H_2, v_3) → R_2
  205. Segment(Q_2, R_2) → g_5