1. The number of circles that are tangent to both circles $(x-a)^{2}-(y-b)^{2}=4\left(a^{2}+b^{2}\right)$, and $(x+a)^{2}+(y+b)^{2}=4\left(a^{2}\right.$ $+b^{2}$ ) and have a radius of $\sqrt{a^{2}+b^{2}}$ is ( ).
A. 2
B. 3
C. 5
D. 7
1. $C$

There are 2 circles that are externally tangent to both circles, 1 circle that is internally tangent to both circles, and 2 circles that are internally tangent to one circle and externally tangent to the other.