Artyom

To tell the truth, I have another problem as a homework, but un case I proof this problem, I will have a solution for my homework problem. All the facts you told about are obvious and they do not help to solve this problem. Oh, I found the solution. It was very obvious, I don't know why I haven't seen it before.

Quadrilateral ABCD is inscribed into a circle. AB is a diameter of this circle. BC crosses AD in point E. E is outside the circle. EH is a perpendicular from E to AB. EH crosses CD in point F. G is a middle of CD. Prove that angles ABG and AFD are equal.