2012 UNCO Math Contest II Problems/Problem 7

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

$4\sqrt{3} - \tfrac{11\pi}{6}$

2012 UNCO Math Contest II (Problems • Answer Key • Resources)
Preceded by Problem 6	Followed by Problem 8
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2012 UNCO Math Contest II Problems/Problem 7

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