Let $\vartriangle ABC$ be an acute triangle, with $\angle A> \angle B \ge \angle C$. Let $D, E$ and $F$ be the tangency points between the incircle of triangle and sides $BC, CA, AB$, respectively. Let $J$ be a point on $(BD)$, $K$ a point on $(DC)$, $L$ a point on $(EC)$ and $M$ a point on $(FB)$, such that $$AF = FM = JD = DK = LE = EA.$$Let $P$ be the intersection point between $AJ$ and $KM$ and let $Q$ be the intersection point between $AK$ and $JL$. Prove that $PJKQ$ is cyclic.