the given circles with the specified point.

We would have this configuration:

the center of the second given circle.

given circle that did not have a specified point. The same distance can be laid off along the line

through the given point from the center of the desired circle, by constructing an additional circle of

the same radius with center at the designated tangent point:

base of this isosceles triangle, as follows, and now we have a construction of the desired circle.

That is, construct a line through the center of the circle with the designated point of tangency and

construct a circle of the same radius as the second of the given circles with the designated point as

center. The intersection of the line and circle will allow construction of the base of the isosceles

triangle and hence allow location of the center of the desired circle. The construction follows.