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Find Length of CE

Source: 1968 AHSME Problem #18

September 7, 2011
geometrysimilar trianglesAMC

Problem Statement

Side ABAB of triangle ABCABC has length 88 inches. Line DEFDEF is drawn parallel to ABAB so that DD is on segment ACAC, and EE is on segment BCBC. Line AEAE extended bisects angle FECFEC. If DEDE has length 55 inches, then the length of CECE, in inches, is:
<spanclass=′latex−bold′>(A)</span> 514<spanclass=′latex−bold′>(B)</span> 13<spanclass=′latex−bold′>(C)</span> 534<spanclass=′latex−bold′>(D)</span> 403<spanclass=′latex−bold′>(E)</span> 272<span class='latex-bold'>(A)</span>\ \dfrac{51}{4} \qquad <span class='latex-bold'>(B)</span>\ 13 \qquad <span class='latex-bold'>(C)</span>\ \dfrac{53}{4} \qquad <span class='latex-bold'>(D)</span>\ \dfrac{40}{3} \qquad <span class='latex-bold'>(E)</span>\ \dfrac{27}{2}
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