Question 3
The circle $\omega_1$ with diameter $[AB]$ and the circle $\omega_2$ with center $A$ intersect at points $C$ and $D$. Let $E$ be a point on the circle $\omega_2$, which is outside $\omega_1$ and at the same side with $C$ with respect to the line $AB$. Let the second point of intersection of the line $BE$ with $\omega_2$ be $F$. Suppose that a point $K \in \omega_1$ is on the same side with $A$ with respect to the diameter of $\omega_1$ passing through $C$ and $2 \cdot CK \cdot AC = CE \cdot AB$. Let the second point of intersection of the line $KF$ with $\omega_1$ be $L$. Show that a point symmetric to $D$ with respect to the line $BE$ lies on the circumcircle of the triangle $LFC$.