Circle with the Same Center as the Incircle of Any Triangle

GeoGebra Commands & Parameters

1. Line(A, B) → f
2. Rotate(B, (a * π / 180), A) → B'
3. Angle(B, A, B') → α
4. Ray(A, B') → g
5. Point(g) → C
6. Segment(B, C) → h
7. Line(A, C) → i
8. Line(C, B) → j
9. Segment(A, B) → k
10. Segment(A, C) → l
11. Min({h, k, l}) → b
12. Angle(C, B, A) → β
13. Rotate(B, α / 2, A) → B'_1
14. Angle(B, A, B'_1) → γ
15. Rotate(C, β / 2, B) → C'
16. Angle(C, B, C') → δ
17. Ray(A, B'_1) → m
18. Ray(B, C') → n
19. Intersect(m, n) → D
20. Segment(D, C) → p
21. Segment(D, A) → q
22. Segment(D, B) → r
23. Max({p, q, r}) → c
24. Circle(D, d) → e
25. Intersect(e, j, 1) → E
26. Intersect(e, i, 2) → F
27. Intersect(e, j, 2) → G
28. Intersect(e, f) → H, I
29. Intersect(e, i, 1) → J
30. Segment(A, D) → s
31. Segment(B, D) → t
32. Min({s, t}) → o
33. Segment(A, B) → f_1
34. Circle(A, (0.35 * o)) → c_1
35. Circle(B, (0.35 * o)) → d_1
36. Intersect(c_1, f_1, 1) → K
37. Intersect(c_1, s, 1) → L
38. Intersect(d_1, h) → M,
39. Intersect(d_1, t, 1) → N
40. Polygon(H, A, J) → poly1, j_1, h_1, a_1
41. Polygon(B, I, G) → poly2, g_1, b_1, i_1
42. Polygon(C, F, E) → poly3, e_1, c_2, f_2
43. Polygon(A, B, C) → poly4, c_3, a_2, b_2
44. Angle(A, C, B) → ε
45. CircleSector(B, M, N) → k_1
46. CircleSector(A, K, L) → p_1
47. Dilate(A, If[0 < u ≤ 1, 1 - u, 0], D) → A'
48. Dilate(B, If[1 < u ≤ 2, 2 - u, 0], D) → B'_2
49. Segment(B, B'_2) → l_1
50. Segment(A, A') → m_1
51. Rotate(p_1, If[2 < u ≤ 3, ((u - 2) * γ), γ], A) → q_1
52. Rotate(k_1, If[3 < u ≤ 4, ((u - 3) * δ), δ], B) → r_1
53. Dilate(D, If[4 < u ≤ 5, 5 - u, 0], F) → D'
54. Circle(D, D') → s_1
55. Segment(D, D') → n_1
56. Dilate(C, If[5 < u ≤ 6, 6 - u, 0], F) → C'_1
57. Dilate(C, If[5 < u ≤ 6, 6 - u, 0], E) → C'_2
58. Dilate(A, If[5 < u ≤ 6, 6 - u, 0], H) → A'_1
59. Dilate(A, If[5 < u ≤ 6, 6 - u, 0], J) → A'_2
60. Dilate(B, If[5 < u ≤ 6, 6 - u, 0], I) → B'_3
61. Dilate(B, If[5 < u ≤ 6, 6 - u, 0], G) → B'_4
62. Segment(C, C'_1) → t_1
63. Segment(C, C'_2) → g_2
64. Segment(A, A'_1) → h_2
65. Segment(A, A'_2) → i_2
66. Segment(B, B'_3) → j_2
67. Segment(B, B'_4) → k_2
68. Dilate(F, If[6 < u ≤ 7, 7 - u, 0], E) → F'
69. Dilate(H, If[6 < u ≤ 7, 7 - u, 0], J) → H'
70. Dilate(G, If[6 < u ≤ 7, 7 - u, 0], I) → G'
71. Segment(F, F') → l_2
72. Segment(H, H') → m_2
73. Segment(G, G') → n_2
74. Rotate(C, If[7 < u ≤ 8, ((u - 7) * ε), ε], C) → C'_3
75. Rotate(C'_1, If[7 < u ≤ 8, ((u - 7) * ε), ε], C) → O
76. Segment(C'_3, O) → p_2
77. Rotate(A, If[8 < u ≤ 9, ((u - 8) * α), α], A) → A'_3
78. Rotate(A'_1, If[8 < u ≤ 9, ((u - 8) * α), α], A) → P
79. Segment(A'_3, P) → q_2
80. Rotate(B, If[9 < u ≤ 10, ((u - 9) * β), β], B) → B'_5
81. Rotate(B'_4, If[9 < u ≤ 10, ((u - 9) * β), β], B) → Q
82. Segment(B'_5, Q) → r_2