\(ABCD\) is a quadrilateral inscribed in a circle with centre \(O\). Let \(BD\) bisect \(OC\) perpendicularly. \(P\) is a point on \(AC\) such that \(PC=OC\). \(BP\) cuts \(AD\) at \(E\) and the circle \(ABCD\) at \(F\). Prove that \(PF\) is the geometric mean of \(EF\) and \(BF\).
This a part of my set NMTC 2nd Level (Junior) held in 2014.