Question 55
Let $ABC$ be an acute angle scalene triangle with $AB \lt AC$, inscribed in the circle $c(O, R)$. The circle $c_1(B, AB)$ intersects the side $AC$ at point $K$ and the circle $c$ at point $E$. The line $KE$ intersects the circle $c$ also at point $F$. The line $BO$ intersects $KE$ at point $L$ and $AC$ at point $M$. Finally, the line $AE$ intersects $BF$ at point $D$. Prove that the polygons $DLMF$ and $BDKME$ are cyclic.