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Intersecting Arcs inside a Square

Source: 1970 AHSME Problem 7

March 21, 2014
AMC

Problem Statement

Inside square ABCDABCD with side ss, quarter-circle arcs with radii ss and centers at AA and BB are drawn. These arcs intersect at point XX inside the square. How far is XX from side CDCD?
<spanclass=′latex−bold′>(A)</span>12s(3+4)<spanclass=′latex−bold′>(B)</span>12s3<spanclass=′latex−bold′>(C)</span>12s(1+3)<span class='latex-bold'>(A) </span>\frac{1}{2}s(\sqrt{3}+4)\qquad<span class='latex-bold'>(B) </span>\frac{1}{2}s\sqrt{3}\qquad<span class='latex-bold'>(C) </span>\frac{1}{2}s(1+\sqrt{3})\qquad
<spanclass=′latex−bold′>(D)</span>12s(3−1)<spanclass=′latex−bold′>(E)</span>12s(2−3)<span class='latex-bold'>(D) </span>\frac{1}{2}s(\sqrt{3}-1)\qquad <span class='latex-bold'>(E) </span>\frac{1}{2}s(2-\sqrt{3})
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