Orthocenter and Geometric Transformations

GeoGebra Commands & Parameters

1. Point(xAxis) → B
2. Rotate(B, (-(40°)), C) → B'
3. Polygon(A, B, C) → t1, c, a, b
4. Slope(c) → m_4
5. Rotate(B, (-γ), C) → C'_{2}
6. CircleArc(C, C'_{2}, B') → r
7. Intersect(r, c) → Q_1,
8. Intersect(r, c, 1) → T
9. Circle(T, u) → d_2
10. Circle(C, a_1) → r_1
11. Rotate(C, 40°, B) → C'
12. Rotate(C, δ, B) → C'_{3}
13. CircleArc(B, C', C'_{3}) → s
14. Intersect(s, b) → R_1,
15. Intersect(r_1, b, 1) → E_1
16. Rotate(E_1, (-ι), C) → H_1
17. Rotate(C, λ, R_1) → C'_{5}
18. Circle(B, u) → c_1
19. Intersect(c_1, c, 1) → R
20. Rotate(R, 40°, B) → R'
21. Rotate(R, ε, B) → R'_{2}
22. CircleArc(B, R', R'_{2}) → d_1
23. Point(Circle[T, u]) → V
24. Rotate(W_1, (-η), T) → V'
25. Rotate(W_1, (-(40°)), T) → T'
26. CircleArc(T, V', T') → h_1
27. Intersect(d_1, h_1, 1) → A_1
28. Segment(C, A_1) → m_1
29. Slope(m_1) → m_2
30. Circle(T, u) → e_1
31. Angle(C, B, C') → α
32. Angle(B', C, B) → β
33. Rotate(B, (-(55°)), C) → B'_{1}
34. Rotate(C, 58°, B) → C'_{1}
35. If(17 ≥ d > 1, B, If[35 > d > 18, C'_{2}, B]) → D
36. If(17 ≥ d > 1, (i, 0), If[d > 35, C'_{3}, If[35 ≥ d > 17, C, (-2, 0)]]) → E
37. Midpoint(D, E) → F
38. LineBisector(D, E) → f
39. Circle(F, 4) → e
40. Intersect(e, f, 2) → G
41. Line(G, D) → g
42. Line(G, E) → h
43. Circle(E, 1) → k
44. Circle(D, 1) → p
45. Circle(G, 0.6) → q
46. Intersect(p, g, 1) → H
47. Intersect(k, h, 1) → I
48. Intersect(q, h) → O, P
49. Intersect(q, g) → J, Q
50. If(15.5 > o > 0, R, If[30 ≥ o ≥ 15.5, R'_{2}, If[o > 30, T, (-3.02484, 1.81287)]]) → L
51. If(30 ≥ o > 0, B, If[31 ≥ o > 30, V, If[o > 31, V', B]]) → K
52. Midpoint(K, L) → M
53. LineBisector(K, L) → m
54. Circle(M, 4) → t
55. Intersect(t, m, 2) → N
56. Rotate(R, 60°, B) → R'_{1}
57. Segment(T, V) → g_1
58. Angle(T', V, T) → ζ
59. If(w > 60, C'_{5}, C) → S
60. If(60 ≥ w > 25, H_1, If[w > 60, R_1, E_1]) → U
61. LineBisector(S, U) → i_1
62. Midpoint(S, U) → W
63. Circle(W, 4) → k_1
64. Intersect(k_1, i_1, 2) → Z
65. Segment(B_1, C) → n_1
66. OrthogonalLine(B_1, n_1) → p_1
67. Circle(B_1, 5) → q_1
68. Intersect(q_1, p_1, 2) → F_1
69. Rotate(E_1, (-(50°)), C) → G_1
70. Angle(G_1, C, E_1) → θ
71. CircleArc(C, H_1, G_1) → s_1
72. Rotate(C, 40°, R_1) → C'_{4}
73. Angle(C, E_1, C'_{4}) → κ
74. CircleArc(R_1, C'_{4}, C'_{5}) → t_1
75. Intersect(s_1, t_1, 1) → J_1
76. Segment(B, J_1) → b_1
77. Slope(b_1) → m_3
78. OrthogonalLine(I_1, b_1) → f_2
79. Circle(I_1, 5) → c_2
80. Intersect(c_2, f_2, 2) → M_1
81. Vector(G, D) → j
82. Vector(G, E) → l
83. Vector(N, K) → n
84. Vector(N, L) → f_1
85. Vector(Z, U) → l_1
86. Vector(Z, S) → j_1
87. Segment(B, I_1) → g_2
88. Intersect(n_1, g_2) → S_1
89. Intersect(c, n_1) → T_1
90. Intersect(g_2, b) → U_1
91. Angle(S_1, T_1, Q_1) → μ
92. Segment(B, J_1) → h_2
93. OrthogonalLine(U_1, b) → i_2
94. Intersect(i_2, a) → V_1
95. Angle(R_1, U_1, V_1) → ν
96. Line(Z_1, xAxis) → j_2