(Solved): In a scalene triangle ABC with centroid G and circumcircle with centre at O. The extension of AG ...

In a scalene triangle $ABC$ with centroid $G$ and circumcircle $?$ with centre at $O$. The extension of $AG$ meets $?$ at M. Lines $AB$ and $CM$ intersect at $P$ and lines $AC$ and $BM$ intersect at $Q$. Suppose the circumcentre $S$ of triangle $APQ$ lies on $?$ and $A,O,S$ are collinear. Prove that $?AGO$ is a right angle.