Question 182
Let $OT$ be a diameter of a circle. Let $A$ and $B$ be two distinct points on the circle both on the same side of $OT$, and let $C$ be the intersection of the tangents to the circle at $A$ and $B$. The tangent to the circle at $T$ meet the lines $OA$, $OB$ and $OC$ at $A'$, $B'$ and $C'$ respectively. Prove that $C'$ is the midpoint of $A'B'$.