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Three Circles (Posted on 2004-07-28) Difficulty: 4 of 5
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?

No Solution Yet Submitted by ThoughtProvoker    
Rating: 3.0000 (3 votes)

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Some Thoughts Soddy's Circles | Comment 1 of 7
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
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