Question 55
Let $D$ be an interior point of a triangle $ABC$ such that $AD = DC$. Let $M$ be the midpoint of $BC$, $N$ be the foot of the perpendicular of $B$ to the line $DM$ and $L$ be the foot of the perpendicular of $N$ to the line $CD$. Prove that the points $A, B, L, N$ lie on a circle.
(Proposed by Khulan Tumenbayar)
(Proposed by Khulan Tumenbayar)