MathDB
The Area of an Incircle of an Incircle

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January 14, 2009
geometryratioLaTeX

Problem Statement

A circle is inscribed in a square, then a square is inscribed in this circle, and finally, a circle is inscribed in this square. What is the ratio of the area of the smaller circle to the area of the larger square? <spanclass=′latex−bold′>(A)</span> π16<spanclass=′latex−bold′>(B)</span> π8<spanclass=′latex−bold′>(C)</span> 3π16<spanclass=′latex−bold′>(D)</span> π4<spanclass=′latex−bold′>(E)</span> π2 <span class='latex-bold'>(A)</span>\ \frac{\pi}{16}\qquad <span class='latex-bold'>(B)</span>\ \frac{\pi}{8}\qquad <span class='latex-bold'>(C)</span>\ \frac{3\pi}{16}\qquad <span class='latex-bold'>(D)</span>\ \frac{\pi}{4}\qquad <span class='latex-bold'>(E)</span>\ \frac{\pi}{2}
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