# Difference in radius of circle

Difference in values of radius of a circle whose centre is at origin and which touches the circle $x^2+y^2 -6x -8y+21=0$ is... I am getting answer $1$ but correct answer is $4$..

The tangent circle $(x-3)^2+(y-4)^2=2^2$ has radius 2, and it is at distance 5 from the origin. A circle centered on the origin will be tangent to it with radius 5-2=3 and with radius 5+2=7 through the line $y=\frac 43 x$. Hence the difference between the two possible tangent circles is 7-3=4.