Two circles $\Gamma _{1}$ and $\Gamma _{2}$ intersect at $M$ and $N$.Let $l$ be the common tangent to $\Gamma _{1}$ and $\Gamma _{2}$ so that $M$ is closer to $l$ than $N$ is.Let $l$ touch $\Gamma _{1}$ at $A$ and $\Gamma _{2}$ at $B$.Let the line through $M$ parallel to $l$ meet the circle $\Gamma _{1}$ again at $C$ and the circle $\Gamma _{2}$ again at $D$.Lines $CA$ and $DB$ meet at $E$;lines $AN$ and $CD$ meet at $P$;lines $BN$ and $CD$ meet at $Q$.Show that $EP=EQ$.

[Though this is an IMO problem,this is not so hard!]