OMM 1998 Problem 5

The tangents at points $B$ and $C$ on a given circle meet at point $A$ . Let $Q$ be a point on segment $AC$ and let $BQ$ meet the circle again at $P$ . The line through $Q$ parallel to $AB$ intersects $BC$ at $J$ . Prove that $PJ$ is parallel to $AC$ if and only if $BC^2 = AC\cdot QC$ .