Assignment 7
Tangent Circles

Given two circles and a point on one of the circles. Construct a circle tangent to the two circles with one point of tangency being the designated point.

Start by constructing a circle.  Label the center A.  Now construct a second circle inside this first circle.  Label the center of the second circle B.

Hide the points used to make the radius of the circle, so as to avoid confusion later.  Put arbitrary points on the smaller and larger circle and label them C and D respectively.   Point D will be the point at which the tangent circle we are about to construct will be tangent to Circle A.

Construct a line through Point A and Point D.  The radius of our tangent circle will lie on segment AD.

Construct segment BC.  Use this segment to construct a circle centered on Point D with radius length BC.

Construct a line segment that has Point B as one endpoint, and the intersection of line AD and Circle D as the other endpoint.

Construct the perpendicular bisector of line BD.  The radius of our tangent circle will be the length of the segment DG.  (G is shown labeled in the next figure.)  This tangent circle will be centered on Point G.  Use these two pieces of information to construct the tangent circle.

The final step to clean up the picture is to hide the lines and circles we used to construct our tangent circle.  You should be left with the original circles (with their centers) and the tangent circle with center G.