Two Special Points of Triangles

GeoGebra Commands & Parameters

1. Midpoint(B, C) → M_{BC}
2. Circle(M_{BC}, C) → c_{ab}
3. Line(B, C) → g_a
4. Polygon(A, B, C) → d_{ABC}, c, a, b
5. Midpoint(A, C) → M_{CA}
6. Circle(M_{CA}, A) → c_{AC}
7. Mirror(B, c_{AC}) → B'
8. LineBisector(B', B) → m_B
9. Mirror(A, c_{ab}) → A'
10. LineBisector(A, A') → m_{AA'}
11. Intersect(m_{AA'}, g_a) → M_A
12. Circle(M_A, A) → c_A
13. Line(A, C) → g_b
14. Intersect(m_B, g_b) → M_B
15. Circle(M_B, B) → c_B
16. If(IsInRegion[Intersect[c_A, c_B, 1], d_{ABC}], Intersect[c_A, c_B, 2], Intersect[c_A, c_B, 1]) → IP_2
17. ToComplex(IP_2) → ip_2
18. Circle(ip_2, 10) → c_{ip2}
19. ToComplex(Intersect[c_{ip2}, c_B, 1]) → pi_0
20. Line(A, B) → g_c
21. Midpoint(B, A) → M_{AB}
22. Circle(M_{AB}, A) → c_{AB}
23. Mirror(C, c_{AB}) → C'
24. LineBisector(C', C) → m_{CC'}
25. Intersect(m_{CC'}, g_c) → M_C
26. Circle(M_C, C) → c_C
27. If(IsInRegion[Intersect[c_A, c_B, 1], d_{ABC}], Intersect[c_A, c_B, 1], Intersect[c_A, c_B, 2]) → IP_1
28. Intersect(c_B, g_b) → W_b, W'_{1}
29. Intersect(c_A, g_a) → W_a, W'_{2}
30. Intersect(c_C, g_c) → W_{2}, W_c
31. Line(B, W_b) → w_β
32. Line(A, W_a) → w_α
33. Line(C, W_{2}) → w'_{1}
34. Line(B, W'_{1}) → w'_β
35. Line(A, W'_{2}) → w'_α
36. Line(C, W_c) → w'_γ
37. Intersect(w'_β, w_α) → W'_a
38. Intersect(w'_α, w'_β) → W'_c
39. Intersect(w_β, w'_α) → W'_b
40. Angle(B, A, C) → α
41. Angle(C, B, A) → β
42. Angle(A, C, B) → γ
43. Mirror(C, w'_α) → C'_{1}
44. Mirror(B, w'_α) → B'_{1}
45. Mirror(C, w'_α) → C'_{2}
46. Mirror(A, w'_α) → A'_{1}
47. Segment(C'_{2}, A'_{1}) → b'
48. Mirror(A, w'_α) → A'_{2}
49. Mirror(B, w'_α) → B'_{2}
50. Segment(A'_{2}, B'_{2}) → c'
51. Mirror(B, w'_α) → B'_{3}
52. Mirror(C, w'_α) → C'_{3}
53. Segment(B'_{3}, C'_{3}) → a'
54. Mirror(g_a, w'_α) → f
55. Line(C'_{1}, C) → g
56. Line(B, B'_{1}) → h
57. Mirror(B, A) → B'_{4}
58. Mirror(C, A) → C'_{4}
59. Point(c_A) → A_0
60. Segment(A_0, B) → i
61. Segment(A_0, C) → j
62. Line(A_0, W_a) → k
63. Angle(B, A_0, W_a) → δ
64. Angle(W_a, A_0, C) → ε
65. Segment(IP_2, p_1) → m
66. Segment(IP_2, p_2) → n
67. Segment(IP_2, p_3) → p
68. Segment(IP_2, p_4) → q
69. Segment(IP_2, p_5) → r
70. Angle(p_1, IP_2, p_2) → η
71. Angle(p_2, IP_2, p_3) → θ
72. Angle(p_3, IP_2, p_4) → ι
73. Angle(p_4, IP_2, p_5) → κ
74. Segment(IP_2, pi_0) → l
75. Angle(pi_0, IP_2, p_1) → ζ
76. Angle(p_5, IP_2, pi_0) → λ