Guest4: Another problem: challenging than the fi..

Posted by: Guest4 October 25, 2007

Another problem: challenging than the first one but could be solved along similar lines.

The circle on the left has a radius of 1 unit and the bigger circle on the right has a radius of 2 unit. The two circles are tangent to each other and a straight line. A third circle, obviously with a smaller radius, is inserted between the other two so that it lies tangent to the two bigger circles and the line. What's the radius of the smallest cricle?

$\begin{picture}(75,40)(-10,-2) \put(0,0){\line(1,0){60}} \put(10,10){\bigcircle{20}} \put(38.3,20){\bigcircle{40}} \put(21.6,3.4){\bigcircle{6.6}} \end{picture}$

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