Question 20
An acute-angled triangle $ABC$ with $AC \gt AB$ is given. The perpendicular bisector of side $BC$ intersects the lines $AC$ and $AB$ at points $D$ and $E$, respectively. The circle with diameter $DE$ intersects the lines $AC$ and $AB$ at points $K$ and $L$, respectively ($K \neq D, L \neq E$). Let $M$ be the midpoint of side $BC$. Prove that the points $K, L$, and $M$ are collinear.