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P21 [Geometry] - Turkish NMO 1st Round - 2014

Source:

May 23, 2014
geometrytrapezoidtrigonometryrectanglegeometric transformationreflectioncircumcircle

Problem Statement

Let ABCDABCD be a trapezoid such that side [AB][AB] and side [CD][CD] are perpendicular to side [BC][BC]. Let EE be a point on side [BC][BC] such that △AED\triangle AED is equilateral. If ∣AB∣=7|AB|=7 and ∣CD∣=5|CD|=5, what is the area of trapezoid ABCDABCD?
<spanclass=′latex−bold′>(A)</span> 273<spanclass=′latex−bold′>(B)</span> 42<spanclass=′latex−bold′>(C)</span> 243<spanclass=′latex−bold′>(D)</span> 40<spanclass=′latex−bold′>(E)</span> 36 <span class='latex-bold'>(A)</span>\ 27\sqrt{3} \qquad<span class='latex-bold'>(B)</span>\ 42 \qquad<span class='latex-bold'>(C)</span>\ 24\sqrt{3} \qquad<span class='latex-bold'>(D)</span>\ 40 \qquad<span class='latex-bold'>(E)</span>\ 36
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