MathDB
Shaded Region in Circles

Source:

February 26, 2008
geometry

Problem Statement

Circles of radius 2 2 and 3 3 are externally tangent and are circumscribed by a third circle, as shown in the figure. Find the area of the shaded region. [asy]unitsize(3mm); defaultpen(linewidth(0.7)+fontsize(8));
filldraw(Circle((0,0),5),grey,black); filldraw(Circle((-2,0),3),white,black); filldraw(Circle((3,0),2),white,black); dot((-2,0)); dot((3,0)); draw((-2,0)--(1,0)); draw((3,0)--(5,0)); label("33",(-0.5,0),N); label("22",(4,0),N);[/asy] <spanclass=latexbold>(A)</span> 3π<spanclass=latexbold>(B)</span> 4π<spanclass=latexbold>(C)</span> 6π<spanclass=latexbold>(D)</span> 9π<spanclass=latexbold>(E)</span> 12π <span class='latex-bold'>(A)</span>\ 3\pi \qquad <span class='latex-bold'>(B)</span>\ 4\pi \qquad <span class='latex-bold'>(C)</span>\ 6\pi \qquad <span class='latex-bold'>(D)</span>\ 9\pi \qquad <span class='latex-bold'>(E)</span>\ 12\pi