Question

Points A,B,C are given on circle Γ such that AB=BC. The tangents at A and at B intersect again at point D. The line CD intersects Γ again at E. The line AE intersects BD at F. If AD=120, what is the length of FB.

Answer 1

This one has been answered before, just before you stopped posting the remainder.

Use intersecting chord properties. The intersection could be inside or outside the circle.
AB and CD are chord which intersect at O (inside or outside the circle).
Then OA*OB=OC*OD