found this problem today and I've been struggling to wrap my head around it. I find it really interesting and if someone would like to give their two cents, I invite you to do so.
heres the problem:
Two circles of radius R are tangent to each other. A line is drawn tangent to both circles, externally. A third circle is drawn so that it is tangent to the two circles as well as the tangent line. The radius of this smaller circle is r. What is the ratio of the circumfrances and the area's for the big to small circles?