Question bank/JEE Advanced/Mathematics

Let $O$ be the centre of the circle $x^{2}+y^{2}=r^{2}$, where $r>\frac{\sqrt{5}}{2}$. Suppose $P Q$ 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 $O P Q$ lies on the line $x+2 y=4$, then what is the value of $r$?

Source: JEEBench (IIT Delhi) / JEE Adv 2020 Paper 2