Dynamic Illustration of a Circle Tangent to a Semicircle and Its Diameter

GeoGebra Commands & Parameters

1. Semicircle(A, B) → c
2. Segment(A, B) → f
3. Point(c) → D
4. Midpoint(f) → E
5. Segment(E, B) → g
6. Rotate(A, 45°, D) → A'
7. Angle(A, D, A') → α
8. Ray(D, A') → h
9. Intersect(f, g) → C
10. Intersect(h, f) → F
11. OrthogonalLine(F, f) → i
12. LineBisector(D, F) → j
13. Intersect(i, j) → G
14. Circle(G, D) → d
15. Point(c) → H
16. Rotate(A, 45°, H) → A'_1
17. Angle(A, H, A'_1) → β
18. Ray(H, A'_1) → k
19. Min(Distance[H, f], Distance[D, G]) → b
20. Segment(H, A) → l
21. Circle(H, (0.5 * b)) → e
22. Intersect(e, l, 1) → I
23. Dilate(A, If[0 < a ≤ 1, 1 - a, 0], H) → A'_2
24. Segment(A, A'_2) → m
25. Dilate(B, If[0 < a ≤ 1, 1 - a, 0], H) → B'
26. Segment(B, B') → n
27. Intersect(f, k) → J
28. Intersect(e, k, 1) → K
29. Circle(K, Distance[H, K]) → p
30. Intersect(p, k, 2) → L
31. Dilate(H, If[1 < a ≤ 2, 2 - a, 0], L) → H'
32. Segment(H, H') → q
33. Rotate(I, If[1 < a ≤ 2, ((a - 1) * π / 4), π / 4], H) → I'
34. CircleSector(H, I, I') → r
35. Rotate(r, If[3 < a ≤ 4, ((a - 3) * π / 4), π / 4], H) → r'
36. Dilate(A, If[4 < a ≤ 5, 5 - a, 0], D) → A'_3
37. Dilate(F, If[4 < a ≤ 5, 5 - a, 0], D) → B'_1
38. Segment(A, A'_3) → s
39. Segment(F, B'_1) → t
40. Line(D, n) → f_1
41. Point(f_1) → M
42. Angle(F, D, M) → γ
43. Dilate(H, If[5 < a ≤ 6, 6 - a, 0], D) → H'_1
44. Vector(H, H'_1) → u
45. Translate(r', u) → r''
46. Rotate(r'', If[5 < a ≤ 6, ((-(a - 5)) * γ), (-γ)], H'_1) → r'''