Let $ABCD$ be a rhombus. Let $K$ be a point on the line $CD$, other than $C$ or $D$, such that $AD = BK$. Let $P$ be the point of intersection of $BD$ with the perpendicular bisector of $BC$. Prove that $A, K$ and $P$ are collinear.
Problem
Source: Tournament of Towns 2007 - Fall - Junior A-Level - P1
Tags: geometry, circumcircle, perpendicular bisector, geometry proposed