$BE$ is the altitude of acute triangle $ABC$. The line $\ell$ touches the circumscribed circle of the triangle $ABC$ at point $B$. A perpendicular $CF$ is drawn from $C$ on line $\ell$. Prove that the lines $EF$ and $AB$ are parallel.
Source: 2015 Latvia BW TST P5
Tags: geometry, parallel, circumcircle
$BE$ is the altitude of acute triangle $ABC$. The line $\ell$ touches the circumscribed circle of the triangle $ABC$ at point $B$. A perpendicular $CF$ is drawn from $C$ on line $\ell$. Prove that the lines $EF$ and $AB$ are parallel.