Given an acute triangle $ABC$ with $AB<AC$, let $D$ be the foot of altitude from $A$ to $BC$ and let $M\neq D$ be a point on segment $BC$.$\,J$ and $K$ lie on $AC$ and $AB$ respectively such that $K,J,M$ lies on a common line perpendicular to $BC$. Let the circumcircles of $\triangle ABJ$ and $\triangle ACK$ intersect at $O$. Prove that $J,O,M$ are collinear if and only if $M$ is the midpoint of $BC$. Proposed by Wong Jer Ren