Touching circles and an overlapping rectangle.

Geometry Level 3

The radius of the smaller circle in the figure below is 6 units and the area of the overlapping rectangle is 243 sq units.

How many units is the radius of the larger circle?

Note: The yellow line segment represents the radius of the larger circle.


The answer is 13.5.

Vijay Simha by Vijay Simha , 47, USA

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1 solution

Marta Reece
Aug 31, 2017

243 = R × ( r + 6 ) 2 − ( R − 6 ) 2 243=R\times\sqrt{(r+6)^2-(R-6)^2}

Solution: R = 27 2 = 13.5 R=\dfrac{27}2=\boxed{13.5}

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