Balkan MO 2014,G5
Let $ABCD$ be a trapezoid inscribed in the circle $\Gamma$ with $AB$ as diameter.$AC\cap BD=E$.The circle with radius $BE$ and center $B$ intersects $\Gamma$ at points $K$ and $L$.Let $M$ be a point so that $M$ lies on $CD$ and $ME\perp BD$.Prove that $KM\perp LD$
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Re: Balkan MO 2014,G5
Prove that $E$ is the incentre of $\Delta DKL$ .