Question 20
Let $H$ be the orthocentre of the acute triangle $ABC$ and let $D$ be a point inside the triangle $ABH$. A line that passes through the point $D$ and is parallel to the line $AH$ intersects the segments $BC$ and $AB$ at $K$ and $L$. A line that passes through the point $D$ and is parallel to the line $BH$ intersects the segments $AC$ and $AB$ at $M$ and $N$. Prove that $C, D$ and $H$ lie on the same line if $K, L, M$ and $N$ lie on the same circle.