MathDB
Circles in Circles

Source: 2018 AMC 8 #15

November 20, 2018
AMC 8geometry2018 AMC 8circles2018 AMC

Problem Statement

In the diagram below, a diameter of each of the two smaller circles is a radius of the larger circle. If the two smaller circles have a combined area of 11 square unit, then what is the area of the shaded region, in square units?
[asy] size(4cm); filldraw(scale(2)*unitcircle,gray,black); filldraw(shift(-1,0)*unitcircle,white,black); filldraw(shift(1,0)*unitcircle,white,black); [/asy]
<spanclass=′latex−bold′>(A)</span>14<spanclass=′latex−bold′>(B)</span>13<spanclass=′latex−bold′>(C)</span>12<spanclass=′latex−bold′>(D)</span>1<spanclass=′latex−bold′>(E)</span>π2<span class='latex-bold'>(A) </span> \frac{1}{4} \qquad <span class='latex-bold'>(B) </span> \frac{1}{3} \qquad <span class='latex-bold'>(C) </span> \frac{1}{2} \qquad <span class='latex-bold'>(D) </span> 1 \qquad <span class='latex-bold'>(E) </span> \frac{\pi}{2}
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