Dynamic Illustration of a Problem by Alexander Bogomolny

GeoGebra Commands & Parameters

1. Segment(A, D) → f
2. Circle(C, f) → e
3. Line(C, D) → m
4. Intersect(e, m) → H, I
5. CircleArc(C, I, H) → p
6. Point(p) → B
7. Line(D, B) → g_1
8. Segment(B, D) → n
9. Dilate(A, If[0 < a ≤ 1, 1 - a, 0], D) → A'
10. Segment(A, A') → s
11. Line(C, s) → c
12. Segment(D, C) → g
13. Midpoint(g) → N
14. Segment(C, B) → h
15. Segment(B, A) → i
16. Midpoint(i) → M
17. Segment(N, M) → j
18. Segment(A, C) → k
19. Intersect(k, n) → L
20. Line(B, f) → l
21. Line(A, h) → q
22. Intersect(l, q) → K
23. Segment(L, K) → r
24. Slope(j) → m_1
25. Slope(r) → m_2
26. Dilate(D, If[1 < a ≤ 2, 2 - a, 0], N) → B'
27. Segment(D, B') → t
28. Dilate(N, If[2 < a ≤ 3, 3 - a, 0], C) → F'
29. Segment(N, F') → b
30. Rotate(D, If[3 < a ≤ 4, ((a - 3) * π), π], N) → B'_1
31. Rotate(B', If[3 < a ≤ 4, ((a - 3) * π), π], N) → B''
32. Intersect(g_1, c) → M_1
33. Angle(M_1, C, B) → α
34. Segment(B'_1, B'') → t'
35. Dilate(D, If[4 < a ≤ 5, 5 - a, 0], C) → B'_2
36. Vector(D, B'_2) → u
37. Translate(A, u) → A'_1
38. Translate(A', u) → A''
39. Segment(A'_1, A'') → s'
40. Rotate(A'_1, If[5 < a ≤ 6, ((a - 5) * α), α], C) → K_1
41. Rotate(A'', If[5 < a ≤ 6, ((a - 5) * α), α], C) → A'''
42. Segment(K_1, A''') → s''
43. Dilate(A, If[6 < a ≤ 7, 7 - a, 0], M) → A'_2
44. Segment(A, A'_2) → d
45. Dilate(M, If[7 < a ≤ 8, 8 - a, 0], B) → E'
46. Segment(M, E') → f_1
47. Rotate(A, If[8 < a ≤ 9, ((a - 8) * π), π], M) → A'_3
48. Rotate(A'_2, If[8 < a ≤ 9, ((a - 8) * π), π], M) → L_1
49. Segment(A'_3, L_1) → d'
50. Polygon(A, D, C, B) → poly1, a_1, b_1, c_1, d_1
51. Dilate(N, If[9 < a ≤ 10, 10 - a, 0], M) → F'_1
52. Segment(N, F'_1) → h_1
53. Circle(C, 5) → e_1
54. Intersect(e_1, m, 1) → N_1
55. Ray(C, N_1) → i_1
56. Intersect(m, q) → O
57. Segment(D, O) → j_1
58. Segment(O, N) → k_1
59. Min(j_1, k_1) → o
60. Circle(C, (0.25 * o)) → p_1
61. Intersect(p_1, i_1, 1) → P
62. Intersect(p_1, s'', 1) → Q
63. Angle(Q, C, P) → β
64. Rotate(Q, If[10 < a ≤ 11, ((a - 10) * β), β], C) → Q'
65. CircleSector(C, Q, Q') → q_1
66. Dilate(A, If[11 < a ≤ 12, 12 - a, 0], K) → A'_4
67. Segment(A, A'_4) → l_1
68. Dilate(C, If[12 < a ≤ 13, 13 - a, 0], O) → C'
69. Vector(C, C') → v
70. Translate(q_1, v) → r_1
71. Intersect(m, l) → R
72. Line(D, A) → n_1
73. Circle(D, 5) → s_1
74. Intersect(s_1, n_1, 1) → S
75. Ray(D, S) → t_1
76. Segment(N, R) → f_2
77. Segment(R, C) → g_2
78. Min(f_2, g_2) → w
79. Circle(D, (0.25 * w)) → c_2
80. Intersect(c_2, t_1, 1) → U
81. Intersect(c_2, m) → T, V
82. Angle(T, D, U) → γ
83. Rotate(T, If[13 < a ≤ 14, ((a - 13) * γ), γ], D) → T'
84. CircleSector(D, T, T') → d_2
85. Dilate(D, If[15 < a ≤ 16, 16 - a, 0], R) → B'_3
86. Vector(D, B'_3) → u_1
87. Translate(d_2, u_1) → e_2
88. Dilate(B, If[14 < a ≤ 15, 15 - a, 0], K) → D'
89. Segment(B, D') → h_2
90. Intersect(m, r) → W
91. Circle(W, (0.6 * Distance[W, N])) → k_2
92. Dilate(A, If[16 < a ≤ 17, 17 - a, 0], L) → A'_5
93. Dilate(B, If[16 < a ≤ 17, 17 - a, 0], L) → D'_1
94. Segment(A, A'_5) → i_2
95. Segment(B, D'_1) → j_2
96. Line(K, W) → l_2
97. Intersect(k_2, l_2) → Z, A_1
98. Intersect(k_2, m) → B_1, C_1
99. Dilate(L, If[17 < a ≤ 18, 18 - a, 0], D) → G'
100. Dilate(L, If[17 < a ≤ 18, 18 - a, 0], C) → G'_1
101. Segment(L, G') → n_2
102. Segment(L, G'_1) → p_2
103. Dilate(L, If[18 < a ≤ 19, 19 - a, 0], K) → G'_2
104. Segment(L, G'_2) → q_2
105. Angle(A_1, W, B_1) → δ
106. Rotate(A_1, If[19 < a ≤ 20, ((a - 19) * δ), δ], W) → D_1
107. CircleSector(W, A_1, D_1) → r_2
108. Dilate(W, If[20 < a ≤ 21, 21 - a, 0], N) → W'
109. Vector(W, W') → v_1
110. Translate(r_2, v_1) → s_2