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Section of Right Triangle

Source: 2015 AMC 10A #19

February 4, 2015
geometrytrigonometrysymmetrytrig identitiesLaw of SinesanglesAMC

Problem Statement

The isosceles right triangle ABCABC has right angle at CC and area 12.512.5. The rays trisecting ∠ACB\angle{ACB} intersect ABAB at DD and EE. What is the area of △CDE\triangle{CDE}?
<spanclass=′latex−bold′>(A)</span>523<spanclass=′latex−bold′>(B)</span>503−754<spanclass=′latex−bold′>(C)</span>1538<spanclass=′latex−bold′>(D)</span>50−2532<spanclass=′latex−bold′>(E)</span>256<span class='latex-bold'>(A) </span>\frac{5\sqrt{2}}{3}\qquad<span class='latex-bold'>(B) </span>\frac{50\sqrt{3}-75}{4}\qquad<span class='latex-bold'>(C) </span>\frac{15\sqrt{3}}{8}\qquad<span class='latex-bold'>(D) </span>\frac{50-25\sqrt{3}}{2}\qquad<span class='latex-bold'>(E) </span>\frac{25}{6}
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