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Dynamic Rhombus & Incircle Illustration

Dynamic Rhombus & Incircle Illustration
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2017-03-10 11:36
CirclePolygonTrigonometryGeometric Construction
In collections Polygons & Angles Polygons & Angles ( s n attar) Polygons & Angles
This example dynamically illustrates the geometric properties of a rhombus and its inscribed circle, involving concepts like symmetry, circle properties, angle calculations, and geometric transformations. It uses commands such as Line, Circle, Intersect, Rotate, and Dilate. Suitable for high school mathematics education to enhance spatial reasoning and understanding of geometric transformations and properties.

GeoGebra Commands & Parameters

  1. Line(A, B) → b
  2. Circle(A, B) → c
  3. Intersect(c, b, 2) → C
  4. CircleArc(A, B, C) → d
  5. Point(d) → D
  6. Circle(D, A) → e
  7. Segment(D, B) → s
  8. Circle(B, A) → f
  9. Intersect(e, f, 2) → E
  10. Angle(D, E, B) → β
  11. Angle(E, B, A) → α
  12. Segment(A, E) → n
  13. Intersect(n, s) → L
  14. Rotate(L, If[13 < l ≤ 14, ((-(l - 13)) * π), -3.141592653589793], L) → L'_2
  15. Dilate(L, If[12 < l ≤ 13, 13 - l, 0], E) → L'_1
  16. Segment(L, L'_1) → j_1
  17. Dilate(L, If[10 < l ≤ 11, 11 - l, 0], B) → L'
  18. Rotate(L', If[13 < l ≤ 14, ((-(l - 13)) * π), -3.141592653589793], L) → L''
  19. Segment(L'_2, L'') → l_1
  20. Rotate(B, If[1 < l ≤ 2, ((-(l - 1)) * α), α], B) → B'_1
  21. Rotate(B'_1, If[2 < l ≤ 3, ((-(l - 2)) * β), (-β)], E) → J
  22. Rotate(J, If[3 < l ≤ 4, ((-(l - 3)) * α), (-α)], D) → J'
  23. Dilate(B, If[0 < l ≤ 1, 1 - l, 0], A) → B'
  24. Rotate(B', If[1 < l ≤ 2, ((-(l - 1)) * α), (-α)], B) → B''
  25. Rotate(B'', If[2 < l ≤ 3, ((-(l - 2)) * β), (-β)], E) → B'''
  26. Rotate(B''', If[3 < l ≤ 4, ((-(l - 3)) * α), (-α)], D) → K
  27. Segment(J', K) → m'''
  28. Segment(J, B''') → m''
  29. OrthogonalLine(L, m'') → n_1
  30. Intersect(n_1, m'') → B_1
  31. Circle(L, B_1) → g_2
  32. Intersect(g_2, j_1) → I_1,
  33. Intersect(g_2, l_1) → H_1,
  34. Intersect(g_2, m''', 1) → C_1
  35. Segment(C_1, I_1) → a_2
  36. Segment(B'_1, B'') → m'
  37. Intersect(g_2, m', 1) → E_1
  38. Segment(H_1, E_1) → t_2
  39. Intersect(a_2, t_2) → Q_1
  40. Segment(A, B) → a
  41. Segment(A, D) → g
  42. Segment(D, E) → h
  43. Segment(E, B) → i
  44. Min(g, h) → j
  45. Segment(B, B') → m
  46. Circle(B, (0.2 * j)) → k
  47. Circle(E, (0.2 * j)) → p
  48. Intersect(p, m'', 1) → F
  49. Intersect(p, m', 1) → G
  50. Intersect(k, m', 1) → H
  51. Intersect(k, m, 1) → I
  52. CircleSector(B, H, I) → q
  53. CircleSector(E, F, G) → r
  54. Polygon(A, B, E, D) → poly1, a_1, b_1, e_1, d_1
  55. Dilate(B, If[5 < l ≤ 6, 6 - l, 0], D) → B'_2
  56. Vector(B, B'_2) → u
  57. Translate(q, u) → q'
  58. Rotate(q', If[6 < l ≤ 7, ((l - 6) * π), 3.141592653589793], D) → q''
  59. Dilate(E, If[7 < l ≤ 8, 8 - l, 0], A) → E'
  60. Vector(E, E') → v
  61. Translate(r, v) → r'
  62. Rotate(r', If[8 < l ≤ 9, ((-(l - 8)) * π), -3.141592653589793], A) → r''
  63. Dilate(D, If[9 < l ≤ 10, 10 - l, 0], L) → D'
  64. Vector(D, D') → w
  65. Min(n / 2, s / 2) → o
  66. Circle(L, (0.2 * o)) → t
  67. Intersect(t, s, 2) → M
  68. Intersect(t, n, 2) → N
  69. CircleSector(L, M, N) → c_1
  70. Segment(D, D') → f_1
  71. Circle(D, (0.2 * j)) → h_1
  72. Intersect(k, s) → P,
  73. Intersect(s, f_1) → Q
  74. Intersect(h_1, s, 1) → O
  75. Circle(A, (0.2 * j)) → k_1
  76. Intersect(k_1, m, 1) → R
  77. Intersect(k_1, n, 1) → S
  78. Intersect(k_1, m''', 1) → T
  79. Intersect(h_1, m'', 1) → U
  80. CircleSector(D, O, U) → q_1
  81. Dilate(A, If[11 < l ≤ 12, 12 - l, 0], L) → A'
  82. Segment(A, A') → i_1
  83. Intersect(p, m'', 1) → V
  84. Intersect(p, n, 1) → W
  85. CircleSector(A, S, T) → s_1
  86. CircleSector(B, P, I) → p_1
  87. Intersect(p, m', 1) → Z
  88. CircleSector(E, W, Z) → r_1
  89. Segment(L, L') → g_1
  90. Rotate(L, If[14 < l ≤ 15, ((-(l - 14)) * π), 3.141592653589793], L) → L'_3
  91. Rotate(L'_1, If[14 < l ≤ 15, ((-(l - 14)) * π), 3.141592653589793], L) → A_1
  92. Segment(L'_3, A_1) → m_1
  93. Rotate(q_1, If[15 < l ≤ 16, ((-(l - 15)) * α / 2), ((-α)) / 2], D) → t_1
  94. Rotate(p_1, If[15 < l ≤ 16, ((-(l - 15)) * α / 2), ((-α)) / 2], B) → c_2
  95. Rotate(s_1, If[16 < l ≤ 17, ((-(l - 16)) * β / 2), ((-β)) / 2], A) → d_2
  96. Rotate(r_1, If[16 < l ≤ 17, ((-(l - 16)) * β / 2), ((-β)) / 2], E) → e_2
  97. Rotate(c_1, If[17 < l ≤ 18, ((l - 17) * π / 2), 1.5707963267948966], L) → f_2
  98. Intersect(g_2, m, 1) → D_1
  99. Segment(L, D_1) → h_2
  100. Dilate(L, If[20 < l ≤ 21, 21 - l, 0], D_1) → L'_4
  101. Segment(L, L'_4) → i_2
  102. Line(L, m) → j_2
  103. Point(j_2) → F_1
  104. Angle(D, L, F_1) → γ
  105. Dilate(L, If[21 < l ≤ 22, 22 - l, 0], D_1) → L'_5
  106. Vector(L, L'_5) → u_1
  107. Translate(f_2, u_1) → k_2
  108. Rotate(k_2, If[22 < l ≤ 23, ((l - 22) * γ), γ], D_1) → p_2
  109. Rotate(D_1, If[23 < l ≤ 24, (((l - 23) * 2) * π), (2 * π)], L) → G_1
  110. CircleArc(L, D_1, G_1) → q_2
  111. Angle(D_1, L, E_1) → δ
  112. Circle(D_1, (0.2 * o)) → r_2
  113. Intersect(r_2, m) → J_1, K_1
  114. Rotate(B, 45°, D_1) → B'_3
  115. Angle(B, D_1, B'_3) → ε
  116. Ray(D_1, B'_3) → l_2
  117. Intersect(m', l_2) → M_1
  118. Intersect(r_2, l_2, 1) → N_1
  119. Dilate(D_1, If[24 < l ≤ 25, 25 - l, 0], M_1) → L_1
  120. Segment(D_1, L_1) → m_2
  121. Intersect(r_2, i_2) → O_1,
  122. CircleSector(D_1, N_1, O_1) → s_2
  123. Dilate(C_1, If[25 < l ≤ 26, 26 - l, 0], Q_1) → P_1
  124. Segment(C_1, P_1) → n_2
  125. Dilate(Q_1, If[26 < l ≤ 27, 27 - l, 0], I_1) → R_1
  126. Segment(Q_1, R_1) → b_2
  127. Dilate(E_1, If[27 < l ≤ 28, 28 - l, 0], Q_1) → S_1
  128. Segment(E_1, S_1) → f_3
  129. Dilate(Q_1, If[28 < l ≤ 29, 29 - l, 0], H_1) → T_1
  130. Segment(Q_1, T_1) → g_3
  131. Rotate(s_2, If[30.5 < l ≤ 31.5, ((-(l - 30.5)) * π / 4), ((-π)) / 4], D_1) → c_3
  132. Line(Q_1, m_2) → h_3
  133. Point(h_3) → U_1
  134. Angle(I_1, Q_1, U_1) → θ
  135. Dilate(D_1, If[32 < l ≤ 33, 33 - l, 0], Q_1) → V_1
  136. Vector(D_1, V_1) → v_1
  137. Translate(c_3, v_1) → d_3
  138. Rotate(d_3, If[33 < l ≤ 34, ((-(l - 33)) * θ), (-θ)], Q_1) → e_3

AI Drawing Prompt Reference

Draw a rhombus ABCD with points A, B, C, and D as its vertices. Draw a circle centered at A with radius AB, intersecting the diagonals at point E. Draw another circle centered at D with radius DA, intersecting the first circle at point F. Use rotation and dilation operations to construct the incircle of the rhombus, intersecting the sides and diagonals to form a series of auxiliary lines and points, ultimately creating the intersection points of the incircle with the sides and diagonals of the rhombus.
The prompt above was compiled from the original drawing commands and is for reference only.