Question 28
Let $\triangle ABC$ be a scalene triangle with $AB \lt AC$, with circumcircle $c(O, R)$. The circle $c_1(A, AB)$ intersects the side $BC$ at $E$ and the circle $c$ at $F$. The line $EF$ meets for a second time the circle $c$ at point $D$ and the side $AC$ at point $M$. The line $AD$ intersects the side $BC$ at point $K$. Finally, the circumcircle of the triangle $BKD$ intersects $AB$ at $L$. Prove that the points $K, L, M$ lie on a line parallel to the line $BF$.