Question 46
Let $\triangle ABC$ be an acute triangle, with $\widehat{A} \gt \widehat{B} \geq \widehat{C}$. Let $D$, $E$ and $F$ be the tangency points between the incircle of the 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.
$$
AF = FM = JD = DK = LE = EA
$$
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.