Question 78
Let $D$ and $E$ be such points on the sides $BC$ and $AC$ of a triangle $ABC$, respectively, that the points $A$, $B$, $D$ and $E$ lie on the same circle. Let $L$ denote the center of the inscribed circle of the triangle $BCE$, and let $G$ denote the point of tangency of this inscribed circle with the side $EC$. Let $K$ denote the center of the inscribed circle of the triangle $DCA$, and let $F$ denote the point of tangency of this inscribed circle with the side $DC$. Let $N$ be the intersection point of the lines $EL$ and $DK$, and let $M$ be the intersection point of the lines $KF$ and $LG$. Prove that the points $A$, $B$, $D$ and $N$ lie on the same circle and that $KMLN$ is a deltoid.