USAJMO 2011 Problem 5

Points $A,B,C,D,E$ lie on a circle $\omega$ and point $P$ lies outside the circle. The given points are such that (i) lines $PB$ and $PD$ are tangent to $\omega$ , (ii) $P, A, C$ are collinear, and (iii) $DE \parallel AC$ . Prove that $BE$ bisects $AC$ .