1. The 2 circles must intersect therefore ..........That means you have to calculate first the radii and the distance between the 2 centers.
2. The tangent of the first circle must pass through the center of the second circle and the tangent of the second circle must pass threough the center of the first circle to get perpendicular tangents. (see attachment)
3. Thus ......... After a few steps of transformation you should get the given result.
4. Good luck!