Ex. 100. Lines $\ell_{1}$ and $\ell_{2}$ are external tangents to two non-intersecting circles, and the distance between the points of tangency on each of these lines is $a$. The internal tangent intersects $\ell_{1}$ and $\ell_{2}$ at points $A$ and $B$. Find the length of segment $A B$.
Ex. 100. a. Note. Use the fact that tangents to a circle drawn from the same point are equal, and divide the segment $A B$ into parts corresponding to the segments of the tangents.