By Tim Lehman

Assignment 7

For Write-up #7,

we are examining tangent circles. We will primarily examine two given circles and find the circle tangent to both of the circles. Let's start on an easier problem.

We will start with a given circle centered at A and passing through B. Find a circle tangent to this circle (we'll call it circle A) at point P that passes through point D.

The center of the tangent circle is along the line perpendicular to the circle A at point P. Thus, it is on the line AP. Further, we know the center of the tangent circle is equidistant from D and P. By definition, it is therefore on the perpendicular bisector of DP. The center is point X in the diagram below and the tangent circle is in blue.

Now we will examine when, instead of passing through D, that it is tangent to a smaller circle inside circle A. Assume we begin with a circle centered at C and passing through D that is inside circle A. Click here for diagram. We want to construct the tangent circle that is external of the smaller circle, as pictured below. The center of the tangent circle is point X.