Equation of circle $=x^2+y^2+2gx+2fy+c=0$
Now consider a circle having (h,k) as centre and radius a, Equation of this circle is $(x-h)^2+(y-k)^2=a^2$
$\Rightarrow$ Equation of a circle with it's center at (2,1), and radius $r$ is x^2+y^2-4x-2y+5-r^2=0$
The other given circle is $x^2+y^2-2x-6y+6=0$ (Note: it's center can be worked out to be $= (1,3)$
The equation of the common chord can be got by subtracting the above two equations, $\rightarrow$ $2x - 4y+1 = r^2$
This chord is the diameter of the second circle, which means that it's center (1,3) must be a solution of the above equation.
$\Rightarrow 2 \times 1 - 4 \times 3 + 1 = r^2 \rightarrow r^2 = 9 \rightarrow r = 3$