Relationship in a Triangle with Angle Bisector and Special Segments

GeoGebra Commands & Parameters

1. Rotate(A, (a * π / 180), B) → A'
2. Ray(B, A') → g
3. Point(g) → C
4. Ray(B, C) → m_1
5. Point(m_1) → S
6. Midpoint(A, S) → V
7. Dilate(B, If[7 < o ≤ 8, 8 - o, 0], A) → B'_1
8. Vector(B, B'_1) → v
9. Dilate(B, If[5 < o ≤ 6, 6 - o, 0], S) → B'
10. Translate(B', v) → B''
11. Segment(B, B') → h_2
12. Line(A, h_2) → k_2
13. Point(k_2) → T
14. Angle(T, A, C) → ζ
15. Line(C, B) → m_2
16. Angle(A, B, A') → α
17. Segment(B, A) → f
18. Segment(B, C) → h
19. Circle(B, b) → c
20. Intersect(c, f, 1) → D
21. Intersect(c, h, 1) → E
22. CircleSector(B, D, E) → d
23. Segment(C, A) → i
24. Line(C, A) → j
25. Line(A, B) → k
26. OrthogonalLine(C, k) → m
27. Intersect(m, k) → H
28. Circle(C, 2) → e
29. Circle(H, 2) → p
30. Intersect(e, j, 1) → J
31. Ray(C, J) → n
32. Line(C, H) → r
33. Polygon(B, A, C) → poly1, c_1, b_1, a_1
34. Angle(C, A, B) → β
35. Line(C, B) → l
36. OrthogonalLine(A, l) → q
37. Segment(C, H) → s
38. Line(C, H) → t
39. Circle(C, 2) → d_1
40. Circle(H, 2) → e_1
41. Intersect(d_1, t, 1) → L
42. Intersect(e_1, t) → M, N
43. Segment(C, H) → h_1
44. Circle(B, 1) → k_1
45. Circle(A, 1) → p_1
46. Intersect(k_1, k, 2) → P
47. Intersect(p_1, k, 1) → Q
48. Ray(B, P) → i_1
49. Ray(A, Q) → j_1
50. Intersect(k_1, l, 2) → K
51. Circle(C, 2) → q_1
52. Intersect(q_1, l, 1) → R
53. Segment(B, C) → n_1
54. Ray(C, R) → r_1
55. Ray(B, K) → s_1
56. Dilate(A, If[2 < o ≤ 3, 3 - o, 0], S) → A'_1
57. Line(C, A) → n_2
58. Angle(A, C, B) → γ
59. Rotate(A, (-(γ / 2)), C) → A'_2
60. Angle(A'_2, C, A) → ε
61. Ray(C, A'_2) → l_1
62. Segment(B, A) → j_2
63. Intersect(l_1, j_2) → F
64. Segment(C, B) → t_1
65. Segment(C, A) → f_2
66. Min(t_1, f_2) → u
67. Circle(C, (0.2 * u)) → c_2
68. Intersect(c_2, t_1, 1) → G
69. Intersect(c_2, l_1, 1) → I
70. Dilate(C, If[0 < o ≤ 1, 1 - o, 0], F) → C'
71. Segment(C, C') → g_2
72. Rotate(G, If[1 < o ≤ 2, ((o - 1) * ε), ε], C) → G'
73. CircleSector(C, G, G') → d_2
74. Rotate(d_2, If[3 < o ≤ 4, ((o - 3) * ε), ε], C) → e_2
75. Dilate(A, If[4 < o ≤ 5, 5 - o, 0], V) → A'_3
76. Segment(A, A'_3) → f_1
77. Translate(B, v) → B'_2
78. Segment(B'_2, B'') → g_1
79. Angle(A, B, C) → δ
80. Rotate(B'_2, If[7 < o ≤ 8, ((o - 7) * δ), δ], A) → O
81. Rotate(B'', If[8 < o ≤ 9, ((o - 8) * ζ), ζ], A) → B'''
82. Segment(O, B''') → i_2
83. Midpoint(B, B''') → U
84. Dilate(V, If[5 < o ≤ 6, 6 - o, 0], S) → V'
85. Segment(V, V') → l_2
86. Rotate(A, If[6 < o ≤ 7, ((o - 6) * π), π], V) → A'_4
87. Rotate(A'_3, If[6 < o ≤ 7, ((o - 6) * π), π], V) → W
88. Segment(A'_4, W) → p_2
89. Dilate(B, If[9 < o ≤ 10, 10 - o, 0], U) → B'_3
90. Segment(B, B'_3) → q_2
91. Dilate(U, If[10 < o ≤ 11, 11 - o, 0], B''') → U'
92. Segment(U, U') → r_2
93. Rotate(B, If[11 < o ≤ 12, ((-(o - 11)) * π), (-π)], U) → B'_4
94. Rotate(B'_3, If[11 < o ≤ 12, ((-(o - 11)) * π), (-π)], U) → Z
95. Rotate(B, If[11 < o ≤ 12, ((-(o - 11)) * π), (-π)], U) → B'_5
96. Rotate(B'_3, If[11 < o ≤ 12, ((-(o - 11)) * π), (-π)], U) → A_1
97. Segment(B'_5, A_1) → s_2
98. Dilate(U, If[12 < o ≤ 13, 13 - o, 0], V) → U'_1
99. Segment(U, U'_1) → t_2
100. Line(U, V) → a_2
101. Intersect(g_2, a_2) → B_1
102. Segment(U, B_1) → b_2
103. Segment(B_1, F) → f_3
104. Segment(B_1, V) → g_3
105. Min({b_2, f_3, g_3}) → w
106. Circle(B_1, (0.5 * w)) → c_3
107. Intersect(c_3, a_2) → C_1, D_1
108. Intersect(g_2, f_3) → E_1
109. Intersect(g_2, f_3) → F_1
110. Intersect(c_3, g_2) → G_1, H_1
111. Rotate(C_1, If[14 < o ≤ 15, ((o - 14) * π / 2), π / 2], B_1) → I_1
112. CircleSector(B_1, C_1, I_1) → d_3
113. Rotate(d_3, If[16 < o ≤ 17, ((o - 16) * π / 2), π / 2], B_1) → e_3