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P01 [Geometry] - Turkish NMO 1st Round - 2003

Source:

May 6, 2014
geometrypower of a point

Problem Statement

Let ABCABC be a triangle such that ∣AB∣=7|AB|=7, ∣BC∣=8|BC|=8, ∣AC∣=6|AC|=6. Let DD be the midpoint of side [BC][BC]. If the circle through AA, BB and DD cuts ACAC at AA and EE, what is ∣AE∣|AE|?
<spanclass=′latex−bold′>(A)</span> 23<spanclass=′latex−bold′>(B)</span> 1<spanclass=′latex−bold′>(C)</span> 32<spanclass=′latex−bold′>(D)</span> 2<spanclass=′latex−bold′>(E)</span> 3 <span class='latex-bold'>(A)</span>\ \dfrac 23 \qquad<span class='latex-bold'>(B)</span>\ 1 \qquad<span class='latex-bold'>(C)</span>\ \dfrac 32 \qquad<span class='latex-bold'>(D)</span>\ 2 \qquad<span class='latex-bold'>(E)</span>\ 3
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