My goal in this assignment is to construct a circle tangent to the two circles with one point a tangency being the designated point.

First, I will construct two circles and a point on one of the circles. The outer circle will have center B and the inner will have center A. I will pick a movable point on the outer circle and I will create a line through B and the movable point.

Now I will construct another circle with center C and with the same radius as my inner circle.

I will create a line segment from A to D and find the midpoint of that segment (mid). Then I will create a perpendicular line to the segment AD that passes through the midpoint. I am now interested in where the perpendicular line to the segment AD intersects the line through B. I will call this point T.

Now I am ready to construct my tangent circle. I will begin by making a segment from A to T and a segment from T to C. The tangent circle will have center T and radius same as the segment TC.

This is getting pretty messy so I will hide some of the lines to see our final tangent circles!!!

For this investigation I will make a script tool for the tangent circles. The process gets a little confusing because of so many lines and points so this should be very helpful for you.