Construction of Tangent Circle
(smaller given circle internal to tangent)
by
Rita Meyers

To start the construction of a Tangent Circle, we have 2 given circles

We then construct a line through an arbitrary point (we'll call point A) on the large circle and the center of the given circle.

Next construct a circle with the point A being the center and the radius equal to the radius of the smaller circle.
Construct a point (we'll call point B) where the new circle intersects the line internal to the large given circle.

Now construct a line segment from the center of the small given circle to point B. Then take the midpoint of this segment and construct the perpendicular bisector of the segment.

The point (we'll call point C) where the perpendicular bisector intersects the line drawn through point A is the center of the circle tangent to both circles where the smaller circle is external to the tangent circle.

Constructing the circle through point A with point C being the center gives you your tangent circle.