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GoGeometry Action 5!

GoGeometry Action 5!
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2017-03-03 12:40
CircleAngleGeometric Construction
In collections Circles (Theorems)
This dynamic and modifiable geometry problem illustration was posted by Antonino Gutierrez on Twitter. It demonstrates how to construct geometric figures using GeoGebra, involving concepts such as line segments, angles, circles, and polygons. Using commands like Line, Slope, PointIn, Angle, and Segment, users can intuitively understand geometric transformations and construction techniques. Suitable for middle school and above students and teachers.

GeoGebra Commands & Parameters

  1. Line(A, B) → d
  2. Slope(d) → a
  3. PointIn(c) → C
  4. Line(A, C) → e
  5. Line(B, C) → f
  6. Angle(B, A, C) → α
  7. Angle(A, C, B) → β
  8. Angle(C, B, A) → γ
  9. Segment(A, C) → g
  10. Segment(C, B) → h
  11. Segment(B, A) → i
  12. Min(list1) → j
  13. Circle(C, (0.2 * j)) → q
  14. Circle(A, (0.2 * j)) → p
  15. Circle(B, (0.2 * j)) → k
  16. Intersect(q, f, 2) → D
  17. Intersect(q, e, 1) → E
  18. Intersect(q, e, 2) → F
  19. Intersect(p, e, 2) → G
  20. Intersect(p, d, 1) → H
  21. Intersect(k, f, 2) → I_2
  22. Intersect(k, d, 2) → J
  23. Intersect(d, i) → K
  24. Intersect(d, i) → L
  25. Intersect(k, f, 1) → N
  26. Intersect(p, e, 1) → O
  27. Intersect(p, d, 2) → P
  28. Angle(D, C, E) → δ
  29. Angle(O, A, P) → ε
  30. Angle(J, B, I_2) → η
  31. Angle(G, A, H) → θ
  32. Incircle(A, B, C) → r
  33. Center(r) → I
  34. Line(C, I) → l
  35. Line(A, I) → n
  36. Line(B, I) → s
  37. Intersect(e, s) → R
  38. Intersect(d, l) → S
  39. Intersect(f, n) → T
  40. Polygon(A, B, C) → poly1, c_1, a_1, b_1
  41. Rotate(D, δ / 2, C) → D'
  42. Angle(D, C, D') → κ
  43. Rotate(J, η / 2, B) → J'
  44. Angle(J, B, J') → λ
  45. Ray(C, D') → t
  46. Ray(B, J') → e_1
  47. Rotate(O, ε / 2, A) → O'
  48. Angle(O, A, O') → ι
  49. Ray(A, O') → d_1
  50. Segment(C, S) → f_1
  51. Segment(A, T) → g_1
  52. Segment(B, R) → h_1
  53. Intersect(q, f_1, 1) → U
  54. Intersect(q, f, 1) → V
  55. Intersect(p, g_1, 1) → W
  56. Intersect(k, h_1, 1) → Z
  57. CircleSector(C, E, U) → k_1
  58. CircleSector(A, P, W) → q_1
  59. CircleSector(B, I_2, Z) → p_1
  60. Dilate(C, If[0 < m ≤ 1, 1 - m, 0], S) → C'
  61. Segment(C, C') → i_1
  62. Rotate(k_1, If[1 < m ≤ 2, ((m - 1) * β / 2), β / 2], C) → r_1
  63. Dilate(B, If[2 < m ≤ 3, 3 - m, 0], R) → B'
  64. Segment(B, B') → j_1
  65. Rotate(p_1, If[3 < m ≤ 4, ((m - 3) * γ / 2), γ / 2], B) → s_1
  66. Dilate(A, If[4 < m ≤ 5, 5 - m, 0], T) → A'
  67. Segment(A, A') → l_1
  68. Rotate(q_1, If[5 < m ≤ 6, ((m - 5) * α / 2), α / 2], A) → t_1
  69. OrthogonalLine(I, f) → m_1
  70. OrthogonalLine(I, d) → n_1
  71. OrthogonalLine(I, e) → a_2
  72. Intersect(f, m_1) → M
  73. Intersect(d, n_1) → A_1
  74. Intersect(e, a_2) → B_1
  75. Segment(I, M) → b_2
  76. Circle(M, (0.2 * b_2)) → c_2
  77. Intersect(c_2, f, 1) → C_1
  78. Intersect(c_2, b_2, 1) → D_1
  79. Intersect(c_2, f, 2) → E_1
  80. CircleSector(M, E_1, D_1) → d_2
  81. Dilate(I, If[6 < m ≤ 7, 7 - m, 0], M) → Q'
  82. Segment(I, Q') → e_2
  83. Rotate(d_2, If[7.5 < m ≤ 8.5, ((m - 7.5) * π / 2), 1.5707963267948966], M) → f_2
  84. Segment(I, B_1) → g_2
  85. Segment(I, A_1) → h_2
  86. Circle(B_1, (0.2 * g_2)) → k_2
  87. Circle(A_1, (0.2 * h_2)) → p_2
  88. Intersect(k_2, e, 2) → F_1
  89. Intersect(k_2, g_2, 1) → G_1
  90. Intersect(k_2, e, 1) → H_1
  91. Intersect(p_2, d, 2) → I_1
  92. Intersect(p_2, h_2, 1) → J_1
  93. Intersect(p_2, d, 1) → K_1
  94. Dilate(I, If[8.5 < m ≤ 9.5, 9.5 - m, 0], B_1) → Q'_1
  95. Segment(I, Q'_1) → i_2
  96. CircleSector(B_1, H_1, G_1) → q_2
  97. CircleSector(A_1, I_1, J_1) → r_2
  98. Rotate(q_2, If[10 < m ≤ 11, ((m - 10) * π / 2), 1.5707963267948966], B_1) → s_2
  99. Dilate(I, If[11 < m ≤ 12, 12 - m, 0], A_1) → Q'_2
  100. Segment(I, Q'_2) → j_2
  101. Rotate(r_2, If[12.5 < m ≤ 13.5, ((m - 12.5) * π / 2), 1.5708], A_1) → t_2
  102. Angle(M, I, B_1) → ζ
  103. Angle(B_1, I, A_1) → μ
  104. Angle(A_1, I, M) → ν
  105. Rotate(I, If[14 < m ≤ 15, ((m - 14) * ζ), ζ], I) → Q'_3
  106. Rotate(Q', If[14 < m ≤ 15, ((m - 14) * ζ), ζ], I) → Q''
  107. Segment(Q'_3, Q'') → l_2
  108. Rotate(Q'_3, If[15 < m ≤ 16, ((m - 15) * μ), μ], I) → L_1
  109. Rotate(Q'', If[15 < m ≤ 16, ((m - 15) * μ), μ], I) → Q'''
  110. Segment(L_1, Q''') → m_2
  111. Rotate(A_1, If[16 < m ≤ 18, ((m - 16) * π), 6.28319], I) → M'
  112. Intersect(m_1, f) → Q
  113. Circle(I, Q) → d_3
  114. Line(A, B) → n_2
  115. CircleArc(I, A_1, M') → c_3
  116. Segment(I, C) → f_3
  117. Intersect(d_3, f_3) → M_1,
  118. Segment(A, M_1) → g_3
  119. Segment(B, M_1) → h_3
  120. Segment(B_1, M) → i_3
  121. Intersect(h_3, i_3) → O_1
  122. Intersect(f_3, i_3) → P_1
  123. Dilate(I, If[20.5 < m ≤ 21.5, 21.5 - m, 0], M_1) → I'
  124. Segment(I, I') → j_3
  125. Dilate(M_1, If[21.5 < m ≤ 22.5, 22.5 - m, 0], C) → Q_1
  126. Segment(M_1, Q_1) → k_3
  127. Dilate(B, If[22 < m ≤ 23, 23 - m, 0], O_1) → B'_1
  128. Dilate(O_1, If[23 < m ≤ 24, 24 - m, 0], M_1) → S_1
  129. Dilate(P_1, If[26 < m ≤ 27, 27 - m, 0], O_1) → V_1
  130. Dilate(O_1, If[27 < m ≤ 28, 28 - m, 0], M) → W_1
  131. Midpoint(B_1, O_1) → Z_1
  132. Rotate(B_1, If[28 < m ≤ 29, ((m - 28) * π), π], Z_1) → A_2
  133. Line(C, I) → e_3
  134. OrthogonalLine(A, e_3) → f_4
  135. Intersect(e_3, f_4) → F_2
  136. Segment(B_1, M) → q_3
  137. Line(M_1, q_3) → r_3
  138. Segment(C, A) → s_3
  139. Segment(C, B) → t_3
  140. Intersect(r_3, s_3) → G_2
  141. Intersect(r_3, t_3) → H_2
  142. Dilate(B_1, If[19.5 < m ≤ 20.5, 20.5 - m, 0], M) → N_1
  143. Segment(B_1, N_1) → l_3
  144. Angle(I, F_2, A) → ξ
  145. Dilate(I, If[23 < m ≤ 24, 24 - m, 0], F_2) → I'_1
  146. Dilate(A, If[23 < m ≤ 24, 24 - m, 0], F_2) → A'_1
  147. Segment(I, I'_1) → m_3
  148. Segment(A, A'_1) → n_3
  149. Intersect(j_3, l_3) → R_1
  150. Segment(R_1, M_1) → p_3
  151. Circle(R_1, (0.5 * p_3)) → c_4
  152. Intersect(c_4, l_3, 2) → T_1
  153. Intersect(c_4, j_3, 2) → U_1
  154. CircleSector(R_1, T_1, U_1) → d_4
  155. Dilate(M_1, If[24 < m ≤ 25, 25 - m, 0], H_2) → B_2
  156. Dilate(M_1, If[24 < m ≤ 25, 25 - m, 0], G_2) → C_2
  157. Segment(M_1, B_2) → a_3
  158. Segment(M_1, C_2) → b_3
  159. Dilate(R_1, If[25 < m ≤ 26, 26 - m, 0], M_1) → D_2
  160. Vector(R_1, D_2) → u
  161. Translate(d_4, u) → e_4
  162. Dilate(B, If[26 < m ≤ 27, 27 - m, 0], O_1) → B'_2
  163. Segment(B, B'_2) → g_4
  164. Dilate(O_1, If[27 < m ≤ 28, 28 - m, 0], M_1) → E_2
  165. Segment(O_1, E_2) → h_4
  166. Dilate(F_2, If[29 < m ≤ 30, 30 - m, 0], O_1) → J_2
  167. Segment(F_2, J_2) → i_4
  168. Dilate(O_1, If[30 < m ≤ 31, 31 - m, 0], H_2) → K_2
  169. Segment(O_1, K_2) → j_4