# Circles and an isosceles triangle

Let $ABCD, CDEF$ be two cyclic quadrilateral (with circumcircles $\Gamma_1, \Gamma_2$), such that $AE||BF$. Let point $P$ located on the circumscribed circle of $\triangle ADE$ such that, $P$ is an interior point of quadrilateral $ABFE$ and $PB=PF$. Prove that quadrilateral $BFPD$ is cyclic if $AE$ is tangent to circles $\Gamma_1, \Gamma_2$! I proved that line $CD$ bisects segment $AE$. Ok, I'm sure it is about the power of a point. I tried making equations, but it didn't help. Also tried angle hunting...

## locked by Jack D'AurizioFeb 1 '18 at 10:28

This question is locked in view of our policy about contest questions. Questions originating from active contests are locked for the duration of the contest, with answers hidden from view by soft-deletion. Please see the comments below for references to the originating contest.