Triangle and Orthocenter Phenomenon

GeoGebra Commands & Parameters

1. Rotate(A, ((-e) * pi / 180), B) → A'
2. Ray(B, A') → q
3. Point(q) → C
4. Polygon(A, B, C) → poly1, c, a, b
5. Line(A, B) → f
6. Segment(A, C) → g
7. Segment(C, B) → h
8. OrthogonalLine(C, f) → i
9. Intersect(f, i) → D
10. Dilate(C, If[0 < d ≤ 1, 1 - d, 0], D) → C'
11. Segment(C, C') → j
12. Segment(C, D) → k
13. Angle(C, C', A) → α
14. Line(A, C) → l
15. Line(B, C) → m
16. OrthogonalLine(B, l) → n
17. Intersect(l, n) → E
18. Dilate(B, If[1.5 < d ≤ 2.5, 2.5 - d, 0], E) → B'
19. Segment(B, B') → p
20. Angle(B, E, C) → β
21. OrthogonalLine(A, m) → r
22. Intersect(m, r) → F
23. Dilate(A, If[3 < d ≤ 4, 4 - d, 0], F) → A'_{1}
24. Segment(A, A'_{1}) → s
25. Angle(B, F, A) → γ
26. Line(C, D) → t
27. Line(E, B) → f_1
28. Line(A, F) → g_1
29. Intersect(t, f_1) → G
30. Dilate(D, If[5 < d ≤ 6, 6 - d, 0], G) → D'
31. Dilate(E, If[5 < d ≤ 6, 6 - d, 0], G) → E'
32. Dilate(F, If[5 < d ≤ 6, 6 - d, 0], G) → F'
33. Segment(F, F') → h_1
34. Segment(E, E') → i_1
35. Segment(D, D') → j_1
36. Angle(C, B, A) → δ
37. Polygon(C, B, GG) → t1, gg, c_1, b_1
38. Segment(C, GG) → k_1
39. Segment(GG, B) → l_1
40. Segment(B, C) → m_1
41. Line(B, GG) → n_1
42. Intersect(l, n_1) → H
43. Angle(C, H, B) → ε
44. Segment(C, H) → p_1
45. Segment(H, AA) → q_1
46. OrthogonalLine(AA, m) → r_1
47. Intersect(m, r_1) → I
48. Segment(GG, I) → s_1
49. Angle(GG, I, B) → ζ
50. Segment(I, AA) → t_1
51. Line(C, GG) → a_1
52. OrthogonalLine(B, a_1) → d_1
53. Intersect(a_1, d_1) → J
54. Angle(C, J, B) → η
55. Segment(B, J) → e_1
56. Segment(B, AA) → f_2
57. Line(C, B) → g_2
58. Line(A, C) → h_2
59. Polygon(A, B, GG) → t2, i_2, a_2, b_2
60. Line(B, GG) → j_2
61. Line(B, A) → k_2
62. Line(A, GG) → l_2
63. OrthogonalLine(GG, k_2) → m_2
64. Intersect(k_2, m_2) → K
65. Segment(GG, K) → n_2
66. Segment(K, C) → p_2
67. Angle(B, K, GG) → θ
68. OrthogonalLine(B, l_2) → q_2
69. Intersect(q_2, l_2) → L
70. Angle(B, L, A) → ι
71. Segment(B, L) → r_2
72. Segment(B, C) → s_2
73. OrthogonalLine(A, j_2) → t_2
74. Intersect(j_2, t_2) → M
75. Angle(A, M, B) → κ
76. Segment(A, M) → c_2
77. Segment(M, C) → d_2
78. Polygon(A, C, G) → t3, g_3, a_3, c_3
79. Line(A, G) → e_2
80. Line(G, C) → f_3
81. Line(C, A) → h_3
82. OrthogonalLine(C, e_2) → i_3
83. Intersect(e_2, i_3) → N
84. Angle(C, N, G) → λ
85. Segment(C, N) → j_3
86. Segment(N, B) → k_3
87. OrthogonalLine(A, f_3) → l_3
88. Intersect(f_3, l_3) → O
89. Segment(A, O) → m_3
90. Angle(G, O, A) → μ
91. Segment(O, B) → n_3
92. OrthogonalLine(G, h_3) → p_3
93. Intersect(h_3, p_3) → P
94. Angle(G, P, A) → ν
95. Segment(G, P) → q_3
96. Segment(G, B) → r_3