Let the equation of the circle be $x^2+y^2-6x-4y+c=0$
So, the common chord of these $2$ circles is
$2x-4y+16-c=0$
It passes through the centre $\left(\mathrm{2,4}\right)$ of the given circle, so
$4-16+16-c=0\Rightarrow c=4$
Hence, the radius of the circle $=\sqrt{9+4-4}=3$ units