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Circle tangent to three sides of a rectangle

Source: 1970 AHSME Problem 12

March 24, 2014
geometryrectangleAMC

Problem Statement

A circle with radius rr is tangent to sides ABAB, ADAD, and CDCD of rectangle ABCDABCD and passes through the midpoint of diagonal ACAC.The area of the rectangle in terms of rr, is
<spanclass=′latex−bold′>(A)</span>4r2<spanclass=′latex−bold′>(B)</span>6r2<spanclass=′latex−bold′>(C)</span>8r2<spanclass=′latex−bold′>(D)</span>12r2<spanclass=′latex−bold′>(E)</span>20r2<span class='latex-bold'>(A) </span>4r^2\qquad<span class='latex-bold'>(B) </span>6r^2\qquad<span class='latex-bold'>(C) </span>8r^2\qquad<span class='latex-bold'>(D) </span>12r^2\qquad <span class='latex-bold'>(E) </span>20r^2
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