Three circles, whose radii are $a,b,c$ touch each other externally and the tangents at their points of contact meet in a point. Then, the distance of this point from either of points of contact is
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$\displaystyle \sqrt { \frac { abc }{ a+b+c } } $
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$\displaystyle \sqrt { \frac { abc }{ a-b-c } } $
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$\displaystyle 2\sqrt { \frac { abc }{ a+b+c } } $
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None of these
A
Correct answer
Explanation
This is a standard geometry result for the radical center of three mutually tangent circles. The distance from the radical center to the points of contact is sqrt(abc / (a+b+c)).