Question 83
Let $k$ be a circle with mid-point $M$. $T$ is a point on $k$ and $t$ the tangent of $k$ in $T$. $P$ is a point on $t$ with $P \neq T$ and $g$ a line containing $P$ with $g \neq t$. $g$ has the points $U$ and $V$ in common with $k$ ($U \neq V$), and $S$ is the mid-point of the arc $UV$ not containing $T$. $Q$ is the point symmetric to $P$ with respect to $TS$. Prove that $QTUV$ is a trapezoid.