Question 61
Let $\omega$ be the incircle of scalene triangle $ABC$. Let $\omega$ be tangent to $AB$ and $AC$ at points $X$ and $Y$. Construct points $X'$ and $Y'$ on line segments $AB$ and $AC$ respectively such that $AX' = XB$ and $AY' = YC$. Let line $CX'$ intersect $\omega$ at points $P, Q$ such that $P$ is closer to $C$ than $Q$. Also let $R$ be the intersection of lines $CX'$ and $BY'$. Prove that $CP = RX'$.