Question 1
Two circles with centers $O,O'$ intersect at $A,B$. The line $TT'$ is tangent to the first circle at $T$ and to the second at $T'$. The perpendiculars from $T,T'$ meet $OO'$ at $S,S'$. Ray $AS$ meets the first circle again at $R$, and ray $AS'$ meets the second again at $R'$. Prove that $R,B,R'$ are collinear.