IT-CESENATICO 2020 Problem 1

Let $\omega$ be a circle and let $A,B,C,D,E$ be five points on $\omega$ in this order. Define $F=BC\cap DE$ , such that the points $F$ and $A$ are on opposite sides, with regard to the line $BE$ and the line $AE$ is tangent to the circumcircle of the triangle $BFE$ . a) Prove that the lines $AC$ and $DE$ are parallel b) Prove that $AE=CD$