Construction of Tangent Circles

1.  Place an arbitrary point on the given line and construct a perpendicular line through this point.

2.  Using the arbitrary point as the center, construct a circle using the same radius as the given circle.

3.  At the intersections of this circle with the constructed perpendicular line, construct parallel lines to the original given line.

4.  Draw a segment from the center of the original given circle to one of the intersections made in step 3.  Construct the midpoint of this segment.

5.  Construct a perpendicular line to the segment through the midpoint constructed in step 4.  The intersection formed by this line and the perpendicular line through the arbitrary point will be the center of the circle.  The radius of this circle will be the distance from this point to the arbitrary point.  Construct a circle using this center and radius.

6.  To construct the other tangent circle, repeat this process using the other intersection that was not used from step 4.