Question

Let $O$ be the centre of the circle $x ^{2}+ y ^{2}= r ^{2}$, where $r >\frac{\sqrt{5}}{2}$. Suppose $PQ$ is a chord of this circle and the equation of the line passing through $P$ and $Q$ is $2 x +4 y =5$. If the centre of the circumcircle of the triangle OPQ lies on the line $x+2 y=4$, then the value of $r$ is _____

Answer 1

Answer isr = 2