The Mittenpunkt of a Triangle

GeoGebra Commands & Parameters

1. Polygon(A, B, C) → t1, c, a, b
2. AngularBisector(B, A, C) → f
3. AngularBisector(C, B, A) → g
4. AngularBisector(A, C, B) → h
5. OrthogonalLine(A, f) → i
6. OrthogonalLine(B, g) → j
7. OrthogonalLine(C, h) → k
8. Intersect(f, h) → I
9. Intersect(j, k) → I_A
10. Intersect(k, i) → I_B
11. Intersect(i, j) → I_C
12. OrthogonalLine(I_A, a) → l
13. OrthogonalLine(I_B, b) → m
14. OrthogonalLine(I_C, c) → n
15. Intersect(l, a) → D_{1}
16. Intersect(m, b) → E_{1}
17. Intersect(n, c) → F_{1}
18. Intersect(l, n) → M_{1}
19. Circle(I_A, D_{1}) → d
20. Circle(I_B, E_{1}) → e
21. Circle(I_C, F_{1}) → p
22. Midpoint(b) → E
23. Midpoint(c) → F
24. Line(I_B, E) → r
25. Line(I_C, F) → s
26. TriangleCenter(A, B, C, 9) → M
27. Circle(M_{1}, I_A) → t
28. Line(B, C) → f_1
29. Line(C, A) → g_1
30. Line(A, B) → h_1
31. TriangleCenter(A, B, C, 6) → L
32. Line(I, M) → i_1
33. TriangleCenter(A, B, C, 7) → Ge
34. Line(Ge, M) → k_1
35. Midpoint(B, C) → D
36. Line(I_A, D) → l_1
37. Segment(I_A, I_B) → q
38. Segment(I_B, I_C) → m_1
39. Segment(I_C, I_A) → n_1
40. Segment(I_A, M) → p_1
41. Segment(I_B, M) → q_1
42. Segment(I_C, M) → r_1
43. Segment(I_C, C) → s_1
44. Segment(B, I_B) → t_1
45. Segment(I_A, A) → a_1
46. AngularBisector(I_B, I_A, I_C) → j_1
47. Angle(B, C, I_A) → α
48. Angle(B, I_C, A) → γ
49. Angle(I_A, B, C) → β
50. Angle(A, I_B, C) → δ
51. Mirror(F_{1}, M) → H_{1}
52. Mirror(E_{1}, M) → J
53. Conic(F_{1}, J, D_{1}, E_{1}, H_{1}) → μ
54. Mirror(A, M) → A'
55. Mirror(B, M) → B'
56. Mirror(C, M) → C'
57. Conic(A, C', B, A', B') → λ
58. Point(λ) → X
59. Tangent(X, μ) → b_1, c_1
60. Intersect(λ, c_1, 2) → Z
61. Intersect(λ, b_1, 2) → Y
62. Distance(L, G) → LG
63. Distance(G, M) → GM
64. Distance(M, G) → MG
65. Distance(G, Ge) → GGe
66. Distance(I, M) → IM
67. Distance(L, I) → LI
68. TriangleCenter(A, B, C, 4) → H
69. TriangleCenter(A, B, C, 10) → S
70. Line(M, H) → g_2
71. Distance(M, H) → MH
72. Distance(M, S) → MS
73. Tangent(Z, λ) → h_2,
74. ClosestPoint(h_2, X) → P
75. ClosestPoint(h_2, Y) → Q
76. Angle(P, Z, X) → ε
77. Angle(Y, Z, Q) → ζ
78. Tangent(X, λ) → i_2,
79. ClosestPoint(i_2, Y) → R
80. ClosestPoint(i_2, Z) → T
81. Angle(R, X, Y) → η
82. Angle(Z, X, T) → θ
83. Tangent(Y, λ) → j_2,
84. ClosestPoint(j_2, Z) → U
85. ClosestPoint(j_2, X) → V
86. Angle(U, Y, Z) → ι
87. Angle(X, Y, V) → κ
88. Vector(X, Y) → f_2
89. Vector(Y, Z) → d_1
90. Vector(Z, X) → e_1
91. Focus(μ) → K, N
92. Focus(λ) → O, W