A circle \(C\) of radius \(2\) lies in the second quadrant and touches both the coordinate axes. Let \(r\) be the radius…

A circle \(C\) of radius \(2\) lies in the second quadrant and touches both the coordinate axes. Let \(r\) be the radius of a circle that has centre at the point \((2, 5)\) and intersects the circle \(C\) at exactly two points. If the set of all possible values of \(r\) is the interval \((\alpha ,\beta )\) then \(3\beta -2\alpha\) is equal to :

[JEE Main 2025, 22 Jan (Shift 1)]