The radius of the concentric circle touching the line x - y = 0 and the circle $x^2 + y^2$-6x - 2y -3 = 0 is.

Explanation

The radius of the concentric circle touching the straight line x - y = 0, centre (3, 1) of circle $x^2 + y^2$-6x - 2y -3 = 0 equal to perpendicular dropped from the center. Radius of concentric circle = $\frac{3 - 1}{\sqrt{1^2 + 1^2}} = \frac{2}{\sqrt{2}} = \sqrt{2}$