Dynamic Illustration of Incircle and Excircle Collinearity in Right Triangles

GeoGebra Commands & Parameters

1. Intersect(xAxis, yAxis) → A
2. Semicircle(A, B) → c
3. Point(c) → C
4. Polygon(A, C, B) → t1, b, a_1, c_1
5. Angle(B, A, C) → α
6. Rotate(B, α / 2, A) → B'
7. Angle(B, A, B') → β
8. Ray(A, B') → f
9. Rotate(A, π / 4, C) → A'
10. Ray(C, A') → g
11. Ray(A, C) → h
12. Ray(A, B) → i
13. Segment(B, C) → j
14. Intersect(g, f) → D
15. Ray(B, B + (1, 0, 0)) → k
16. Point(k) → E
17. Circle(C, 3) → d
18. Intersect(d, h, 2) → F
19. Angle(E, B, C, xOyPlane) → γ
20. Rotate(E, γ / 2, B) → E'
21. Ray(B, E') → l
22. Rotate(B, π / 4, C) → B'_1
23. Ray(C, B'_1) → m
24. Intersect(l, m) → G
25. OrthogonalLine(D, h) → n
26. OrthogonalLine(D, k, xOyPlane) → p
27. Intersect(n, h) → H
28. Intersect(p, i) → I
29. OrthogonalLine(G, h, xOyPlane) → q
30. OrthogonalLine(G, k, xOyPlane) → r
31. Intersect(q, h) → J
32. Intersect(r, i) → K
33. Circle(G, J, xOyPlane) → e
34. Circle(D, H) → s
35. Ray(B, D) → t
36. Angle(A, C, B) → δ
37. Ray(B, D) → f_1
38. Ray(A, D) → g_1
39. Min({Distance[A, D], Distance[B, D], Distance[B, G], Distance[C, G]}) → o
40. Circle(A, (0.35 * o)) → d_1
41. Intersect(d_1, i) → L,
42. Circle(B, (0.35 * o)) → e_1
43. Circle(C, (0.35 * o)) → h_1
44. Intersect(h_1, h, 2) → M
45. Intersect(k, e_1) → N,
46. Intersect(e_1, j) → O,
47. Dilate(A, If[0 < u ≤ 1, 1 - u, 0], D) → A'_1
48. Segment(A, A'_1) → i_1
49. Dilate(B, If[0 < u ≤ 1, 1 - u, 0], D) → B'_2
50. Segment(B, B'_2) → j_1
51. Rotate(O, If[0 < u ≤ 1, (u * (π / 2 - α) / 2), (π / 2 - α) / 2], B) → O'
52. Rotate(L, If[0 < u ≤ 1, (u * β), β], A) → L'
53. CircleSector(B, O, O') → k_1
54. CircleSector(A, L, L') → p_1
55. Dilate(C, If[1 < u ≤ 2, 2 - u, 0], G) → C'
56. Dilate(B, If[1 < u ≤ 2, 2 - u, 0], G) → B'_3
57. Segment(B, B'_3) → l_1
58. Segment(C, C') → m_1
59. Intersect(h_1, j) → P,
60. Rotate(P, If[1 < u ≤ 2, ((u - 1) * π / 4), π / 4], C) → P'
61. Rotate(N, If[1 < u ≤ 2, ((u - 1) * γ / 2), γ / 2], B) → N'
62. CircleSector(B, N, N', xOyPlane) → q_1
63. CircleSector(C, P, P') → r_1
64. Rotate(p_1, If[2.5 < u ≤ 3.5, ((u - 2.5) * β), β], A) → s_1
65. Rotate(k_1, If[2.5 < u ≤ 3.5, ((u - 2.5) * (π / 2 - α) / 2), (π / 2 - α) / 2], B) → t_1
66. Rotate(q_1, If[3.5 < u ≤ 4.5, ((u - 3.5) * γ / 2), γ / 2], B) → c_2
67. Rotate(r_1, If[3.5 < u ≤ 4.5, ((u - 3.5) * π / 4), π / 4], C) → d_2
68. Dilate(D, If[5 < u ≤ 6, 6 - u, 0], H) → D'
69. Circle(D, D') → e_2
70. OrthogonalLine(D, j) → n_1
71. Intersect(j, n_1) → Q
72. Dilate(G, If[6 < u ≤ 7, 7 - u, 0], J) → G'
73. Circle(G, G', xOyPlane) → f_2
74. OrthogonalLine(G, j, xOyPlane) → b_1
75. Intersect(b_1, j) → R
76. Dilate(H, If[12 < u ≤ 13, 13 - u, 0], R) → H'
77. Segment(H, H') → g_2
78. Dilate(R, If[13 < u ≤ 14, 14 - u, 0], K) → R'
79. Segment(R, R') → h_2