Rhombus Surprise: A Special Angle Revealed

GeoGebra Commands & Parameters

1. Rotate(B, (a * π / 180), A) → B'
2. Ray(A, B') → j
3. Circle(A, B) → c
4. Intersect(c, j) → E,
5. Line(B, E) → m
6. Segment(A, B) → f
7. Circle(B, f) → h
8. Circle(E, f) → d
9. Intersect(d, h, 1) → C
10. Line(A, C) → l
11. Intersect(l, m) → D
12. Segment(E, C) → i
13. OrthogonalLine(D, i) → n
14. Intersect(n, i) → F
15. Circle(D, F) → p
16. Intersect(p, l) → L, M
17. Intersect(p, m) → H, I
18. Angle(M, D, F) → ζ
19. Circle(B, f) → e
20. Angle(B, A, B') → α
21. Segment(A, E) → g
22. Segment(B, C) → k
23. Intersect(n, f) → G
24. Angle(D, G, A) → β
25. OrthogonalLine(D, k) → q
26. Intersect(k, q) → J
27. Segment(I, J) → r
28. OrthogonalLine(D, g) → s
29. Intersect(g, s) → K
30. Segment(K, M) → t
31. Intersect(t, r) → N
32. Segment(D, A) → b
33. Segment(I, D) → f_1
34. Segment(J, N) → g_1
35. Segment(N, M) → h_1
36. Min({f_1, b, g_1, h_1}) → o
37. Circle(D, (0.3 * o)) → c_1
38. Rotate(I, 45°, D) → I'
39. Angle(I, D, I') → γ
40. Ray(D, I') → i_1
41. Intersect(c_1, b, 1) → O
42. Intersect(c_1, i_1, 1) → P
43. Dilate(A, If[0 < u ≤ 1, 1 - u, 0], B) → A'
44. Segment(A, A') → j_1
45. Rotate(A, If[1 < u ≤ 2, ((u - 1) * α), α], A) → A'_1
46. Rotate(A', If[1 < u ≤ 2, ((u - 1) * α), α], A) → A''
47. Segment(A'_1, A'') → k_1
48. Rotate(A'_1, If[2 < u ≤ 3, ((u - 2) * (π - α)), π - α], A) → Q
49. Rotate(A'_1, If[2 < u ≤ 3, ((u - 2) * (π - α)), π - α], E) → R
50. Rotate(A'', If[2 < u ≤ 3, ((u - 2) * (π - α)), π - α], E) → A'''_1
51. Segment(R, A'''_1) → m_1
52. Rotate(R, If[3 < u ≤ 4, ((u - 3) * α), α], C) → R'
53. Rotate(A'''_1, If[3 < u ≤ 4, ((u - 3) * α), α], C) → S
54. Segment(R', S) → l_1
55. Polygon(A, B, C, E) → poly1, r_1, s_1, t_1, a_1
56. Segment(A'', I) → n_1
57. Segment(E, D) → p_1
58. Circle(A, (0.15 * f)) → d_1
59. Segment(A, A'') → q_1
60. Intersect(d_1, q_1) → T,
61. Intersect(d_1, f) → U,
62. CircleSector(A, U, T) → e_1
63. Dilate(A, If[4 < u ≤ 5, 5 - u, 0], D) → A'_2
64. Dilate(E, If[4 < u ≤ 5, 5 - u, 0], D) → E'
65. Segment(A, A'_2) → b_1
66. Segment(A'', E') → f_2
67. Dilate(D, If[5 < u ≤ 6, 6 - u, 0], B) → D'
68. Dilate(D, If[5 < u ≤ 6, 6 - u, 0], C) → D'_1
69. Segment(D, D') → g_2
70. Segment(D, D'_1) → h_2
71. Dilate(D, If[6 < u ≤ 7, 7 - u, 0], G) → D'_2
72. Segment(D, D'_2) → i_2
73. Angle(G, D, J) → δ
74. Angle(J, D, M) → ε
75. Angle(I, D, K) → ρ
76. Angle(K, D, G) → θ
77. Rotate(G, If[7 < u ≤ 8, ((u - 7) * δ), δ], D) → G'
78. CircleArc(D, G, G') → c_2
79. Rotate(J, If[8 < u ≤ 9, ((u - 8) * ε), ε], D) → J'
80. CircleArc(D, J, J') → d_2
81. Rotate(M, If[9 < u ≤ 10, ((u - 9) * ζ), ζ], D) → M'
82. CircleArc(D, M, M') → e_2
83. Angle(F, D, A'') → η
84. Rotate(F, If[10 < u ≤ 11, ((u - 10) * η), η], D) → F'
85. CircleArc(D, F, F') → k_2
86. Rotate(I, If[11 < u ≤ 12, ((u - 11) * ρ), ρ], D) → I'_1
87. CircleArc(D, I, I'_1) → p_2
88. Rotate(K, If[12 < u ≤ 13, ((u - 12) * θ), θ], D) → K'
89. CircleArc(D, K, K') → q_2
90. Dilate(I, If[6 < u ≤ 7, 7 - u, 0], G) → I'_2
91. Dilate(I, If[13 < u ≤ 14, 14 - u, 0], J) → I'_3
92. Segment(I, I'_3) → j_2
93. Dilate(K, If[14 < u ≤ 15, 15 - u, 0], N) → K'_1
94. Segment(K, K'_1) → l_2
95. Dilate(N, If[15 < u ≤ 16, 16 - u, 0], M) → N'
96. Segment(N, N') → m_2
97. Ray(D, P) → n_2
98. Segment(A, A'') → r_2
99. Intersect(r_2, n_2) → V
100. Dilate(D, If[16 < u ≤ 17, 17 - u, 0], V) → O'
101. Segment(D, O') → s_2
102. Rotate(O, If[17 < u ≤ 18, ((-(u - 17)) * π / 4), ((-π)) / 4], D) → O'_1
103. CircleSector(D, O'_1, O) → t_2
104. Rotate(t_2, If[19 < u ≤ 20, ((-(u - 19)) * π / 4), ((-π)) / 4], D) → c_3
105. Line(N, g_2) → a_2
106. Point(a_2) → W
107. Angle(J, N, W) → τ
108. Dilate(D, If[21 < u ≤ 22, 22 - u, 0], N) → D'_3
109. Vector(D, D'_3) → w
110. Translate(c_3, w) → d_3
111. Rotate(d_3, If[22 < u ≤ 23, ((-(u - 22)) * τ), (-τ)], N) → e_3