Incircle Problem with Dynamic Illustration

GeoGebra Commands & Parameters

1. Circle(A_1, A) → c
2. Circle(C_1, A) → d
3. Semicircle(A, D_1) → e
4. Semicircle(D_1, A) → f
5. Point(e) → D_2
6. Segment(A, D_2) → g
7. OrthogonalLine(D_2, h) → i
8. Intersect(h, i) → E
9. Distance(A, g) → distanceAg
10. Intersect(e, j_1, 1) → I
11. Semicircle(A, H) → c_1
12. Circle(D_2, 2) → d_1
13. Circle(D_2, 2) → r_1
14. Segment(A, D_1) → b_1
15. Mirror(cc, y = 0) → cc'
16. Mirror(c_1, y = 0) → e_2
17. Mirror(e, y = 0) → e'
18. Mirror(ee, y = 0) → ee'
19. Point(c) → B
20. Line(D_2, B) → j
21. Intersect(cc', j) → C, F
22. Intersect(cc, j) → D,
23. Segment(A, D_2) → k
24. Segment(A, D) → l
25. Segment(A, C) → n
26. Segment(A, B) → p
27. Circle(A, (0.3 * Min[{p, n, l, k}])) → q
28. Intersect(q, p, 1) → G
29. Intersect(q, n, 1) → J
30. CircleSector(A, G, J) → r
31. Dilate(D_2, If[0 < m ≤ 1, 1 - m, 0], D) → K
32. Segment(D_2, K) → s
33. Dilate(D, If[1 < m ≤ 2, 2 - m, 0], C) → D'
34. Segment(D, D') → t
35. Dilate(C, If[2 < m ≤ 3, 3 - m, 0], B) → C'
36. Segment(C, C') → f_1
37. Dilate(A, If[3 < m ≤ 4, 4 - m, 0], B) → A'
38. Dilate(A, If[3 < m ≤ 4, 4 - m, 0], D_2) → A'_1
39. Segment(A, A'_1) → g_1
40. Segment(A, A') → h_1
41. Segment(A, J) → i_1
42. Dilate(A, If[4 < m ≤ 5, 5 - m, 0], C) → A'_2
43. Dilate(A, If[4 < m ≤ 5, 5 - m, 0], D) → A'_3
44. Segment(A, A'_3) → k_1
45. Segment(A, A'_2) → l_1
46. Angle(C, A, D_2) → α
47. Rotate(r, If[5.5 < m ≤ 6.5, ((m - 5.5) * α), α], A) → r'