Question 10
Let $ABCD$ be a convex quadrilateral such that the triangle $BCD$ is acute and $|AB| = |AD|$. Denote the intersection of the bisector of the angle $\angle CAD$ with the side $CD$ by $K$ and the intersection of the bisector of the angle $\angle BAC$ with the side $BC$ by $L$. Let $K'$ and $L'$ be the orthogonal projections of $K$ and $L$ onto the sides $BC$ and $CD$, respectively. Prove that $B$, $D$, $L'$ and $K'$ are concyclic.