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Reciprocal of circumference

Source: 1978 AHSME Problem 2

May 27, 2014
geometryAMC

Problem Statement

If four times the reciprocal of the circumference of a circle equals the diameter of the circle, then the area of the circle is
<spanclass=′latex−bold′>(A)</span>1π2<spanclass=′latex−bold′>(B)</span>1π<spanclass=′latex−bold′>(C)</span>1<spanclass=′latex−bold′>(D)</span>π<spanclass=′latex−bold′>(E)</span>π2<span class='latex-bold'>(A) </span>\frac{1}{\pi^2}\qquad<span class='latex-bold'>(B) </span>\frac{1}{\pi}\qquad<span class='latex-bold'>(C) </span>1\qquad<span class='latex-bold'>(D) </span>\pi\qquad <span class='latex-bold'>(E) </span>\pi^2
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