Three circles of radius 6, 7, and 8 are externally tangent to each other. There exists a smaller circle tangent to all three (in the space created between the three original circles).

What is the radius of this smallest circle?

This is a case of Soddy's Circles (see http://braden.buzzword.com/mathGems/kissPrecise) or of Descartes' theorem (see http://www.worldhistory.com/wiki/D/Descartes'-theorem.htm), or "osculating" or "kissing" circles ... just do the math as in http://icl.pku.edu.cn/yujs/MathWorld/math/s/s474.htm !

Posted by Oskar on 2004-07-28 12:29:07