Properties of Tangents Drawn to Circles

GeoGebra Commands & Parameters

1. Circle(O, B_1) → c
2. Segment(O, B_1) → a
3. PointIn(b) → E
4. Tangent(E, c) → d, e
5. Intersect(c, e, 1) → B
6. Intersect(c, d, 1) → A
7. Ray(E, A) → f
8. Ray(E, B) → g
9. Segment(O, A) → h
10. Segment(O, B) → i
11. Dilate(O, If[0 < j ≤ 1, 1 - j, 0], A) → A'
12. Dilate(O, If[0 < j ≤ 1, 1 - j, 0], B) → A'_1
13. Segment(O, A') → k
14. Segment(O, A'_1) → l
15. Angle(E, B, O) → α
16. Angle(O, A, E) → β
17. Circle(A, (0.25 * a)) → p
18. Circle(B, (0.25 * a)) → q
19. Intersect(p, h, 1) → F
20. Intersect(q, i, 1) → G
21. Intersect(p, f) → H, I
22. Intersect(q, g) → J, K
23. Circle(O, B_1) → t
24. Dilate(O, If[3.6 < j ≤ 4.6, 4.6 - j, 0], E) → C'
25. Angle(A, E, B) → γ
26. Rotate(B, If[5 < j ≤ 6, ((j - 5) * ((2 * pi) - γ)), (2 * pi) - γ], E) → D'_1
27. Rotate(E, If[5 < j ≤ 6, ((j - 5) * ((2 * pi) - γ)), (2 * pi) - γ], E) → C'_1
28. Segment(E, A) → n
29. Ray(A, I) → m
30. Ray(B, K) → g_1
31. Rotate(E, If[5 < j ≤ 6, ((j - 5) * (-γ)), (-γ)], E) → C'_2
32. Rotate(B, If[5 < j ≤ 6, ((j - 5) * (-γ)), (-γ)], E) → D'
33. Rotate(I, If[1.5 < j ≤ 2.5, ((j - 1.5) * pi / 2), pi / 2], A) → I'
34. Rotate(K, If[1.5 < j ≤ 2.5, ((-(j - 1.5)) * pi / 2), ((-pi)) / 2], B) → K'
35. Dilate(E, If[-1 < j ≤ 0, (-j), 0], A) → E'
36. Dilate(E, If[-1 < j ≤ 0, (-j), 0], B) → E'_1
37. Segment(E, E'_1) → f_1
38. Segment(E, E') → i_1
39. Line(E, A) → j_1
40. Line(E, B) → k_1
41. Circle(B, 2) → p_1
42. Circle(A, 2) → q_1
43. Intersect(q_1, j_1) → C, D
44. Intersect(p_1, k_1) → L, M
45. Ray(A, D) → l_1
46. Ray(B, M) → m_1
47. Rotate(E, If[4.75 < j ≤ 5.75, ((j - 4.75) * γ), γ], E) → E'_2
48. Rotate(E', If[4.75 < j ≤ 5.75, ((j - 4.75) * γ), γ], E) → E''
49. Segment(E'_2, E'') → n_1
50. Angle(O, B, E) → δ
51. Angle(O, A, E) → ε