Dynamic Relationship Among Triangle's Angle Bisector, Orthocenter, and Circumcen

GeoGebra Commands & Parameters

1. Rotate(A, (a * π / 180), B) → A'
2. Angle(A, B, A') → α
3. Segment(A, B) → f
4. Ray(B, A') → g
5. LineBisector(f) → j
6. Rotate(A, α / 2, B) → A'_1
7. Angle(A, B, A'_1) → β
8. Ray(B, A'_1) → n
9. Rotate(B, ((-b) * π / 180), A) → B'
10. Angle(B, A, B') → ε
11. Ray(A, B') → h
12. Intersect(g, h) → C_1
13. Segment(C_1, B) → i
14. Segment(C_1, A) → k
15. LineBisector(f) → l
16. LineBisector(k) → m
17. Intersect(m, l) → C
18. OrthogonalLine(C_1, f) → p
19. OrthogonalLine(B, k) → q
20. Intersect(p, q) → O
21. Rotate(C_1, (b / 2 * π / 180), A) → C'
22. Angle(C_1, A, C') → γ
23. Ray(A, C') → r
24. Rotate(A, α / 2, B) → A'_2
25. Angle(A, B, A'_2) → δ
26. Rotate(C_1, ((b * π / 180) * 0.5), A) → C'_1
27. Angle(C_1, A, C'_1) → ζ
28. Ray(B, A'_2) → s
29. Ray(A, C'_1) → t
30. Intersect(s, t) → I
31. Angle(O, C_1, I) → η
32. Angle(I, C_1, C) → θ
33. Segment(C_1, O) → c
34. Segment(C_1, I) → d
35. Segment(C_1, C) → e
36. Min({c, d, e}) → o
37. Line(C_1, I) → f_1
38. Line(C_1, O) → g_1
39. Line(C_1, C) → h_1
40. OrthogonalLine(C_1, f) → i_1
41. Circle(C_1, (0.4 * o)) → c_1
42. Intersect(c_1, h_1) → E, F
43. Intersect(c_1, i_1) → H, I_1
44. Intersect(c_1, f_1) → G, J
45. Polygon(B, A, C_1) → t1, c_2, b_1, a_1
46. OrthogonalLine(I, f) → j_1
47. Intersect(f, j_1) → K
48. Angle(A, K, I) → ι
49. Intersect(q, Line[A, C_1]) → L
50. Angle(B, L, A) → κ
51. Line(C_1, A) → k_1
52. Line(A, B) → l_1
53. Line(B, C_1) → m_1
54. Intersect(l_1, i_1) → M
55. Angle(A, M, C_1) → λ_1
56. Dilate(C_1, If[0 < u ≤ 1, 1 - u, 0], M) → C'_2
57. Segment(C_1, C'_2) → n_1
58. Dilate(B, If[1 < u ≤ 2, 2 - u, 0], L) → B'_1
59. Segment(B, B'_1) → p_1
60. Dilate(C, If[3.5 < u ≤ 4.5, 4.5 - u, 0], A) → CCTR'
61. Segment(C, CCTR') → q_1
62. Circle(C, CCTR') → d_1
63. Dilate(I, If[5.5 < u ≤ 6.5, 6.5 - u, 0], K) → I'
64. Segment(I, I') → r_1
65. Circle(I, I') → e_1
66. Dilate(C_1, If[10.5 < u ≤ 11.5, 11.5 - u, 0], O) → D
67. Dilate(C_1, If[10.5 < u ≤ 11.5, 11.5 - u, 0], I) → N
68. Dilate(C_1, If[10.5 < u ≤ 11.5, 11.5 - u, 0], C) → P
69. Segment(C_1, D) → s_1
70. Segment(C_1, N) → t_1
71. Segment(C_1, P) → f_2
72. Line(C_1, O) → g_2
73. Line(C_1, I) → h_2
74. Line(C_1, C) → i_2
75. Rotate(I_1, If[12 < u ≤ 13, ((u - 12) * η), η], C_1) → Q
76. CircleSector(C_1, I_1, Q) → d_2
77. Rotate(d_2, If[14 < u ≤ 15, ((u - 14) * η), η], C_1) → e_2
78. Angle(B, C_1, A) → μ
79. Angle(F, C_1, J) → τ
80. Rotate(F, If[12 < u ≤ 13, ((u - 12) * τ), τ], C_1) → F'
81. CircleSector(C_1, F, F') → k_2
82. Rotate(k_2, If[14 < u ≤ 15, ((u - 14) * τ), τ], C_1) → p_2
83. Angle(F, C_1, J) → λ
84. Rotate(F, If[12 < u ≤ 13, ((u - 12) * λ), λ], C_1) → F'_1
85. CircleSector(C_1, F, F'_1) → q_2
86. Rotate(q_2, If[14 < u ≤ 15, ((u - 14) * λ), λ], C_1) → r_2
87. Angle(I_1, C_1, J) → χ
88. Rotate(I_1, If[12 < u ≤ 13, ((u - 12) * χ), χ], C_1) → R
89. CircleSector(C_1, I_1, R) → s_2
90. Rotate(s_2, If[14 < u ≤ 15, ((u - 14) * χ), χ], C_1) → t_2