By Amber Krug
Given two circles and a point on one of the circles, we can construct a circle tangent to the two circles with one point of tangency being the designated point.
This is accomplished by constructing a line between A, the given point, and the center of the first circle. Then, a circle with the same radius as the smaller circle is created with center A. We then draw a line from A to the center of the smaller circle. The intersection of the perpendicular line to this segment at the midpoint of the segment and the line through the center of the larger circle and A is the center of our tangent circle.
I experimented with the placement of A on the larger circle, and I found it interesting that as A approaches the smaller circle, the tangent circle decreases in size, and in fact, the tangent circle is constructed inside the smaller circle. To see an animation of this, click here and hit the “Animate Point” button.