KöMaL 2024 B5394

Let $O$ be the center of square $ABCD$, and let $X$ be an arbitrary point on its circumcircle. Let $T$ denote the orthogonal projection of $X$ onto $BC$. Let $E$ denote the intersection of lines $XB$ and $AC$, and let $F$ denote the intersection of lines $XC$ and $BD$. Prove the $EF$ is perpendicular to $TO$.