Dynamic Relationship Between a Parallelogram's Diagonal and Special Circles

GeoGebra Commands & Parameters

1. Rotate(B, a°, A) → B'
2. Angle(B, A, B') → α
3. Ray(A, B) → f
4. Ray(A, B') → g
5. Line(B, g) → h
6. Point(g) → C
7. Line(C, f) → i
8. Intersect(h, i) → D
9. Segment(C, D) → j
10. Segment(A, B) → k
11. Segment(B, D) → l
12. Segment(A, C) → m
13. Min(m, k) → b
14. Circle(C, (0.2 * b)) → d
15. Circle(A, (0.2 * b)) → e
16. Circle(B, (0.2 * b)) → p
17. Circle(D, (0.2 * b)) → c
18. Intersect(e, k, 1) → E
19. Intersect(e, m, 1) → F
20. Intersect(p, k, 1) → G
21. Intersect(p, l, 1) → H
22. Intersect(d, g, 2) → I
23. Ray(C, I) → q
24. Intersect(c, h, 2) → J
25. Ray(D, J) → r
26. Intersect(c, i, 2) → K
27. Ray(D, K) → s
28. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], B) → A'
29. Segment(A, A') → t
30. Rotate(E, If[1 < o ≤ 2, ((o - 1) * α), α], A) → E'
31. CircleSector(A, E, E') → c_1
32. Dilate(A, If[2 < o ≤ 3, 3 - o, 0], C) → A'_1
33. Vector(A, A'_1) → u
34. Translate(c_1, u) → d_1
35. Segment(A, A'_1) → f_1
36. Dilate(C, If[3 < o ≤ 4, 4 - o, 0], D) → C'
37. Vector(C, C') → v
38. Translate(d_1, v) → e_1
39. Segment(C, C') → g_1
40. Dilate(D, If[4 < o ≤ 5, 5 - o, 0], B) → D'
41. Segment(D, D') → h_1
42. Polygon(A, B, D, C) → poly1, a_1, b_1, d_2, c_2
43. Dilate(A, If[5.5 < o ≤ 6.5, 6.5 - o, 0], C) → A'_2
44. Vector(A, A'_2) → w
45. Translate(A, w) → A'_3
46. Translate(A', w) → A''
47. Dilate(A, If[6.5 < o ≤ 7.5, 7.5 - o, 0], B) → A'_4
48. Vector(A, A'_4) → u_1
49. Translate(A, u_1) → A'_5
50. Translate(A'_1, u_1) → L
51. Intersect(d, i) → M, N
52. Intersect(d, g) → O, P
53. Angle(A, C, N) → β
54. Rotate(N, If[6.5 < o ≤ 7.5, ((-(o - 6.5)) * β), (-β)], C) → N'
55. Dilate(C, If[7.5 < o ≤ 8.5, 8.5 - o, 0], B) → C'_1
56. Vector(C, C'_1) → v_1
57. Midpoint(A, D) → Q
58. Dilate(A, If[5.5 < o ≤ 6.5, 6.5 - o, 0], Q) → A'_6
59. Segment(A, A'_6) → i_1
60. Dilate(Q, If[6.5 < o ≤ 7.5, 7.5 - o, 0], D) → Q'
61. Segment(Q, Q') → j_1
62. Dilate(B, If[7.5 < o ≤ 8.5, 8.5 - o, 0], Q) → B'_1
63. Segment(B, B'_1) → k_1
64. Dilate(Q, If[8.5 < o ≤ 9.5, 9.5 - o, 0], C) → Q'_1
65. Segment(Q, Q'_1) → l_1
66. Rotate(A, If[9.5 < o ≤ 10.5, ((-(o - 9.5)) * π), (-π)], Q) → A'_7
67. Rotate(A'_6, If[9.5 < o ≤ 10.5, ((-(o - 9.5)) * π), (-π)], Q) → R
68. Rotate(B, If[10.5 < o ≤ 11.5, ((-(o - 10.5)) * π), (-π)], Q) → B'_2
69. Rotate(B'_1, If[10.5 < o ≤ 11.5, ((-(o - 10.5)) * π), (-π)], Q) → S
70. Circle(A, Q, B) → p_1
71. Ray(A, B) → q_1
72. LineBisector(B, A) → r_1
73. LineBisector(A, Q) → s_1
74. Intersect(r_1, s_1) → T
75. Line(T, Q) → t_1
76. OrthogonalLine(Q, t_1) → f_2
77. Intersect(f_2, q_1) → U
78. Circle(D, Q, U) → e_2
79. Intersect(e_2, q_1) → V, W
80. Distance(D, W) → distanceDW
81. Distance(C, B) → distanceCB
82. LineBisector(U, D) → m_1
83. LineBisector(D, Q) → g_2
84. Intersect(g_2, m_1) → Z
85. Dilate(T, If[10.5 < o ≤ 11.5, 11.5 - o, 0], Q) → T'
86. Circle(T, T') → h_2
87. Dilate(Z, If[12.5 < o ≤ 13.5, 13.5 - o, 0], D) → Z'
88. Dilate(T, If[11.5 < o ≤ 12.5, 12.5 - o, 0], Q) → T'_1
89. Segment(T, T'_1) → n_1
90. Line(Q, U) → i_2
91. Circle(Q, 3) → k_2
92. Intersect(k_2, i_2, 1) → A_1
93. Angle(A_1, Q, T) → γ
94. Ray(Q, A_1) → j_2
95. Dilate(Q, If[12.5 < o ≤ 13.5, 13.5 - o, 0], U) → Q'_2
96. Segment(Q, Q'_2) → l_2
97. Dilate(B, If[12.5 < o ≤ 13.5, 13.5 - o, 0], U) → B'_3
98. Segment(B, B'_3) → m_2
99. Dilate(Z, If[14.5 < o ≤ 15.5, 15.5 - o, 0], D) → Z'_1
100. Circle(Z, Z'_1) → p_2
101. Dilate(D, If[16 < o ≤ 17, 17 - o, 0], W) → D'_1
102. Segment(D, D'_1) → n_2
103. Line(W, l_1) → q_2
104. Point(q_2) → B_1
105. Angle(D, W, B_1) → δ
106. Rotate(D, If[17 < o ≤ 18, ((o - 17) * δ), δ], W) → D'_2
107. Rotate(D, If[18 < o ≤ 19, ((o - 18) * δ), δ], W) → D'_3
108. Rotate(D'_1, If[18 < o ≤ 19, ((o - 18) * δ), δ], W) → C_1
109. Segment(D'_3, C_1) → r_2
110. Dilate(W, If[19 < o ≤ 20, 20 - o, 0], B) → W'
111. Vector(W, W') → w_1
112. Translate(D'_3, w_1) → D_1
113. Translate(C_1, w_1) → E_1
114. Segment(D_1, E_1) → s_2
115. Ray(A, B) → t_2
116. Circle(B, 2) → c_3
117. Intersect(c_3, t_2, 2) → F_1
118. Ray(B, F_1) → a_2