**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.