Question 9
Let $O$ be the point of intersection of two diagonals of a square $ABCD$. Points $P, Q, R, S$ lie on the line segments $OA, OB, OC, OD$, respectively, and satisfy $OP = 3$, $OQ = 5$, $OR = 4$. Here we denote for a line segment $XY$ its length also by $XY$. If the point of intersection of lines $AB$ and $PQ$, the point of intersection of lines $BC$ and $QR$, and the point of intersection of lines $CD$ and $RS$ are collinear, what is the value of $OS$?
