BD-BDMO 2019 Problem 3

Let $\alpha$ and $\omega$ be two circles such that $\omega$ goes through the center of $\alpha$ . $\omega$ intersects $\alpha$ at $A$ and $B$ .Let $P$ any point on the circumference $\omega$ .The lines $PA$ and $PB$ intersects $\alpha$ again at $E$ and $F$ respectively.Prove that $AB=EF$ .