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2012 UNCO Math Contest II Problems/Problem 7

Revision as of 02:21, 17 October 2014 by Timneh (talk | contribs) (Created page with "== Problem == A circle of radius <math>1</math> is externally tangent to a circle of radius <math>3</math> and both circles are tangent to a line. Find the area of the shaded r...")
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Problem

A circle of radius $1$ is externally tangent to a circle of radius $3$ and both circles are tangent to a line. Find the area of the shaded region that lies between the two circles and the line.

[asy] draw((-1,-1)--(7,-1),black); filldraw((0,-1)--(0,0)--(2*sqrt(3),2)--(2*sqrt(3),-1)--cycle,grey); filldraw(circle((0,0),1),white); filldraw(circle((2*sqrt(3),2),3),white); [/asy]

Solution

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