KöMaL 2017 B4889

The trapezium $ABCD$ has an inscribed circle. The circle touches base $AB$ at point $T$, and the parallel base $CD$ at point $U$. Let $M$ denote the intersection of the lines of legs $AD$ and $BC$, and let $V$ be the intersection of side $AB$ with line $MU$. Show that $AT=VB$.