Locus of a Point at a Fixed Distance from a Line Segment

GeoGebra Commands & Parameters

1. Dilate(B, Path / Distance[A, B], A) → P_1
2. Rotate(B, 90°, A) → B'
3. Segment(B', A) → g
4. Circle(A, d) → c
5. Intersect(c, g) → C,
6. Vector(A, C) → w
7. Segment(A, B) → a
8. Circle(B, d) → e
9. OrthogonalLine(B, a) → b
10. OrthogonalLine(A, a) → f
11. Rotate(A, 90°, B) → A'
12. Vector(A, B') → u
13. Vector(B, A') → v
14. Segment(B, A') → h
15. Intersect(e, h) → E,
16. Vector(B, E) → z
17. Translate(A, z) → F
18. Translate(B, z) → B'_1
19. Segment(F, B'_1) → a'
20. Translate(A, w) → A'_2
21. Translate(B, w) → D
22. Segment(A'_2, D) → a'_1
23. CircleArc(B, E, D) → k
24. CircleArc(A, C, F) → p
25. Translate(P_1, w) → G
26. Vector(P_1, G) → i
27. Rotate(D, (-180° * (Path - Distance[A, B]) / Distance[A, B]), B) → D_θ
28. Vector(B, D_θ) → j
29. Dilate(A, (Path - (2 * Distance[A, B])) / Distance[A, B], B) → P_3
30. Translate(P_3, z) → H
31. Vector(P_3, H) → l
32. Rotate(F, (-180° * (Path - (3 * Distance[A, B])) / Distance[A, B]), A) → F_θ
33. Vector(A, F_θ) → m
34. Segment(C, G) → q
35. Segment(C, D) → r
36. CircleArc(B, D_θ, D) → s
37. CircleArc(B, E, D) → t
38. Segment(E, H) → a_1
39. Segment(E, F) → b_1
40. CircleArc(A, F_θ, F) → c_1