A circle \(C\) touches the line \(x=2 y\) at the point \((2,1)\) and intersects the circle \(C_1: x^2+y^2+2 y-5=0\) at t…

A circle \(C\) touches the line \(x=2 y\) at the point \((2,1)\) and intersects the circle \(C_1: x^2+y^2+2 y-5=0\) at two points \(P\) and \(Q\) such that \(P Q\) is a diameter of \(C_1\). Then the diameter of \(C\) is

[JEE Main 2021, 26 Aug (Shift 2)]