Question 88
Let $c(O, R)$ be a circle and let $A, B$ be two points on the circle such that $R \lt AB \lt 2R$. The circle $c_1(A, r)$, $0 \lt r \lt R$, meets the circle $c(O, R)$ at points $C$ and $D$ ($C$ belongs to the small arch $\widehat{AB}$). From point $B$ we draw the tangents $BE$ and $BF$ to the circle $c_1(A, r)$, such that $E$ lies outside of the circle $c(O, R)$. The lines $EC$ and $DF$ intersect at $M$. Prove that the quadrilateral $BCFM$ is cyclic.
(E. Psychas)
(E. Psychas)