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Points on Semicircles

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April 6, 2013
geometrytrapezoid

Problem Statement

Let ABAB be a segment of length 2626, and let points CC and DD be located on ABAB such that AC=1AC=1 and AD=8AD=8. Let EE and FF be points on one of the semicircles with diameter ABAB for which ECEC and FDFD are perpendicular to ABAB. Find EFEF.
<spanclass=′latex−bold′>(A)</span>5<spanclass=′latex−bold′>(B)</span>52<spanclass=′latex−bold′>(C)</span>7<spanclass=′latex−bold′>(D)</span>72<spanclass=′latex−bold′>(E)</span>12<span class='latex-bold'>(A) </span>5\qquad<span class='latex-bold'>(B) </span>5\sqrt2\qquad<span class='latex-bold'>(C) </span>7\qquad<span class='latex-bold'>(D) </span>7\sqrt2\qquad<span class='latex-bold'>(E) </span>12
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