On the chord $AB$ of the circle $\omega$ points $C$ and $D$ are chosen such that $AC=BD$ and point $C$ lies between $A$ and $D$. On $\omega$ point $E$ and $F$ are marked, they lie on different sides with respect to line $AB$ and lines $EC$ and $FD$ are perpendicular to $AB$. The angle bisector of $AEB$ intersects line $DF$ at $R$ Prove that the circle with center $F$ and radius $FR$ is tangent to $\omega$ V. Kamenetskii, D. Bariev