Question 16
Let $ABC$ be an acute non-isosceles triangle with circumcentre $O$ and incentre $I$. Its incircle touches $BC,CA,AB$ at $D,E,F$, respectively. Let $P=AI\cap OD$, $Q=BI\cap OE$, $R=CI\cap OF$, and let $M$ be the circumcentre of $PQR$. Prove that $I,M,O$ are collinear.