Question 37
Let $P$ be inside triangle $ABC$. Lines $AP,BP,CP$ meet its circumcircle again at $T,S,R$, respectively, with $T\ne A,S\ne B,R\ne C$. Let $U$ lie in the interior of segment $PT$. The line through $U$ parallel to $AB$ meets $CR$ at $W$, and the line through $U$ parallel to $AC$ meets $BS$ at $V$. The line through $B$ parallel to $CP$ and the line through $C$ parallel to $BP$ meet at $Q$. Given $RS\parallel VW$, prove that $\angle CAP=\angle BAQ$.
