Dynamic Proof of Incenters in Isosceles Triangle Divided by Cevian

GeoGebra Commands & Parameters

1. Rotate(A, (a * π / 180), B) → A'
2. Angle(A, B, A') → α
3. Rotate(B, ((-a) * π / 180), A) → B'
4. Ray(B, A') → f
5. Ray(A, B') → g
6. Intersect(f, g) → C
7. Segment(B, A) → h
8. Polygon(B, A, C) → t1, c, b, a_1
9. OrthogonalLine(C, h) → i
10. Intersect(i, h) → H
11. Point(h) → D
12. Segment(C, D) → j
13. Angle(A, D, C) → β
14. Rotate(A, β / 2, D) → A'_1
15. Angle(A, D, A'_1) → γ
16. Ray(D, A'_1) → k
17. Rotate(C, (a * π / 360), A) → C'
18. Angle(C, A, C') → δ
19. Ray(A, C') → l
20. Intersect(k, l) → F_1
21. Rotate(A, α / 2, B) → A'_2
22. Angle(A, B, A'_2) → ε
23. Ray(B, A'_2) → m
24. Rotate(C, (π - β) / 2, D) → C'_1
25. Angle(C, D, C'_1) → ζ
26. Ray(D, C'_1) → n
27. Intersect(m, n) → G
28. OrthogonalLine(G, h) → p
29. OrthogonalLine(F_1, h) → q
30. Intersect(p, h) → E
31. Intersect(q, h) → F
32. Distance(E, H) → distanceHD
33. Distance(D, F) → distanceEI
34. Distance(D, E) → distanceDE
35. Distance(H, F) → distanceHF
36. Angle(B, C, D) → η
37. Angle(D, C, A) → θ
38. Dilate(B, If[0 < d ≤ 1, 1 - d, 0], C) → B'_1
39. Segment(B, B'_1) → r
40. Rotate(B, If[1 < d ≤ 2, ((d - 1) * (η + θ)), η + θ], C) → B'_2
41. Rotate(B'_1, If[1 < d ≤ 2, ((d - 1) * (η + θ)), η + θ], C) → I
42. Segment(B'_2, I) → r'
43. Angle(C, H, B) → ι
44. Segment(C, H) → s
45. Segment(E, B) → t
46. Segment(F, A) → e
47. Min({s, t, e}) → o
48. Dilate(C, If[3 < d ≤ 4, 4 - d, 0], D) → C'_2
49. Segment(C, C'_2) → f_1
50. Circle(C, (0.3 * o)) → c_1
51. Circle(B, (0.3 * o)) → d_1
52. Circle(A, (0.3 * o)) → e_1
53. Segment(B, C) → g_1
54. Segment(C, D) → h_1
55. Intersect(p, g_1) → J
56. Intersect(f_1, h_1) → K
57. Intersect(c_1, h_1) → L,
58. Intersect(d_1, g_1) → M,
59. Segment(C, A) → i_1
60. Intersect(e_1, i_1) → N,
61. Dilate(C, If[4 < d ≤ 5, 5 - d, 0], G) → C'_3
62. Dilate(B, If[4 < d ≤ 5, 5 - d, 0], G) → B'_3
63. Segment(B, B'_3) → k_1
64. Segment(C, C'_3) → l_1
65. Rotate(M, If[5 < d ≤ 6, ((-(d - 5)) * ε), (-ε)], B) → M'
66. Rotate(J, If[5 < d ≤ 6, ((d - 5) * η / 2), η / 2], C) → J'
67. CircleSector(B, M', M) → p_1
68. Rotate(p_1, If[7 < d ≤ 8, ((-(d - 7)) * ε), (-ε)], B) → s_1
69. Rotate(L, If[5 < d ≤ 6, ((-(d - 5)) * η / 2), ((-η)) / 2], C) → L'
70. CircleSector(C, L', L) → q_1
71. Rotate(q_1, If[7 < d ≤ 8, ((-(d - 7)) * η / 2), ((-η)) / 2], C) → r_1
72. Polygon(B, D, C) → t2, c_2, b_1, d_2
73. Polygon(D, A, C) → t3, c_3, d_3, a_2
74. Rotate(L, If[9 < d ≤ 10, ((d - 9) * θ / 2), θ / 2], C) → L'_1
75. Rotate(N, If[9 < d ≤ 10, ((d - 9) * δ), δ], A) → N'
76. Dilate(C, If[8 < d ≤ 9, 9 - d, 0], F_1) → C'_4
77. Dilate(A, If[8 < d ≤ 9, 9 - d, 0], F_1) → A'_3
78. Segment(C, C'_4) → j_1
79. Segment(A, A'_3) → m_1
80. CircleSector(C, L, L'_1) → t_1
81. CircleSector(A, N, N') → e_2
82. Rotate(t_1, If[11 < d ≤ 12, ((d - 11) * θ / 2), θ / 2], C) → f_2
83. Rotate(e_2, If[11 < d ≤ 12, ((d - 11) * δ), δ], A) → g_2
84. Dilate(C, If[13 < d ≤ 14, 14 - d, 0], H) → C'_5
85. Segment(C, C'_5) → n_1
86. Angle(G, E, B) → κ
87. Angle(A, F, F_1) → λ
88. Dilate(G, If[14 < d ≤ 15, 15 - d, 0], E) → G'
89. Dilate(F_1, If[14 < d ≤ 15, 15 - d, 0], F) → O
90. Segment(G, G') → h_2
91. Segment(F_1, O) → i_2
92. Dilate(D, If[15 < d ≤ 16, 16 - d, 0], F) → D'
93. Segment(D, D') → j_2
94. Distance(B, D) → u
95. Distance(B, A) → v
96. Midpoint(E, F) → P
97. Rotate(D, If[16 < d ≤ 17, ((-(d - 16)) * π), (-π)], P) → D'_1
98. Rotate(D', If[16 < d ≤ 17, ((-(d - 16)) * π), (-π)], P) → D''
99. Segment(D'_1, D'') → k_2
100. Dilate(D, If[15 < d ≤ 16, 16 - d, 0], E) → D'_2
101. Segment(D, D'_2) → l_2
102. Rotate(D, If[16 < d ≤ 17, ((d - 16) * π), π], P) → D'_3
103. Rotate(D'_2, If[16 < d ≤ 17, ((d - 16) * π), π], P) → Q
104. Segment(D'_3, Q) → m_2