Investigations with Tangent Circles

Karyn Carson

To construct a circle tangent to two others, we first construct the two circles, A and B:

Next, letŐs draw a line (CD)that passes through the center of the larger circle, A, to use for the center of the tangent circle:

Next, weŐll need to construct a radius for circle B (letŐs call it BE) so that we can mark off points on line CD (using the intersection of line CD and circle A) that are congruent to the radius of circle B.  We need this because the center of the tangent circle will be equidistant from one of the given circles (B) and one of the constructed circles from BŐs radius (letŐs call this circle K):

Now, construct a segment from the center of B and the center of circle K and mark itŐs midpoint:

Construct the perpendicular bisector of segment BK and mark the intersection of it and line CD.  Because this point is equally distant from the center of circle B and the new circle, this is the center of the tangent circle (T).

Now construct the tangent circle.

If we look at just the circles, we see that circle T is tangent to both A and B.

HereŐs the script: