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

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

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