Tangent Circles with Equal Radii, Line Is Tangent and Perpendicular to the Line Connecting Centers

Steps

1. The centers of all circles tangent to both given circles, but not at their common point of tangency, lie on the perpendicular bisector of the segment connecting their centers.
2. The distance between the given line and a parallel line through the perpendicular bisector determines the radius of the solution circles. The centers of circles externally tangent to the given circles therefore lie on a circle whose center is the center of the given circle, and whose radius is the sum of the radius of the given circle and the distance between the two parallel lines.
3. One solution circle has its center at the point of tangency of the given circles. The other two centers lie at the intersections of the constructed circle and the line.
4. The problem has three solutions.