Existence of the Orthocenter in a Right Triangle

GeoGebra Commands & Parameters

1. Dilate(A, If[0 < t < 1, 1 - t, 0], C) → A_{1}
2. Vector(A, C) → u
3. Translate(B, u) → B'
4. Vector(B, C) → v
5. Translate(A, v) → A'
6. Dilate(B, If[0 < t < 1, 1 - t, 0], B') → B_{1}
7. Segment(A_{1}, B_{1}) → f
8. Dilate(B, If[1 < t < 2, 2 - t, 0], C) → B_{2}
9. Dilate(A, If[1 < t < 2, 2 - t, 0], A') → A_{2}
10. Segment(A_{2}, B_{2}) → g
11. Dilate(B, If[2 < t < 3, 3 - t, 0], A) → B_{3}
12. Dilate(C, If[2 < t < 3, 3 - t, 0], A') → C_{3}
13. Segment(C_{3}, B_{3}) → h
14. Vector(C, A) → w
15. Translate(B, w) → B'_1
16. Dilate(C, If[3 < t < 4, 4 - t, 0], A) → C_{4}
17. Dilate(B, If[3 < t < 4, 4 - t, 0], B'_1) → B_{4}
18. Segment(C_{4}, B_{4}) → i
19. Dilate(A, If[4 < t < 5, 5 - t, 0], B'_1) → A_{5}
20. Dilate(C, If[4 < t < 5, 5 - t, 0], B) → C_{5}
21. Segment(C_{5}, A_{5}) → j
22. Dilate(A, If[5 < t ≤ 6, 6 - t, 0], B) → A_{6}
23. Dilate(C, If[5 < t < 6, 6 - t, 0], B') → C_{6}
24. Segment(A_{6}, C_{6}) → k
25. Polygon(A, B, C) → poly1, c, a, b
26. OrthogonalLine(C, c) → l
27. OrthogonalLine(A, a) → m
28. OrthogonalLine(B, b) → n
29. Intersect(l, n) → D
30. Line(B, A) → p
31. Intersect(p, l) → E
32. Line(B, C) → q
33. Line(A, C) → r
34. Intersect(r, n) → F
35. Intersect(m, q) → G
36. Segment(A, E) → s
37. Angle(A, E, C) → α
38. Segment(C, G) → e
39. Angle(A, G, B) → β
40. Segment(A, F) → f_1
41. Angle(B, F, C) → γ
42. Rotate(A', If[7 < t, (-((360° * t))), 0], D) → A''
43. Angle(A'', D, A') → δ
44. Dilate(D, If[6 < t < 7, 7 - t, 0], A'') → D'
45. CircleArc(D, A'', A') → c_1
46. Segment(D, D') → g_1