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P17 [Geometry] - Turkish NMO 1st Round - 2014

Source:

May 23, 2014
geometryratiotrigonometry

Problem Statement

Let EE be the midpoint of side [AB][AB] of square ABCDABCD. Let the circle through BB with center AA and segment [EC][EC] meet at FF. What is ∣EF∣/∣FC∣|EF|/|FC|?
<spanclass=′latex−bold′>(A)</span> 2<spanclass=′latex−bold′>(B)</span> 32<spanclass=′latex−bold′>(C)</span> 5−1<spanclass=′latex−bold′>(D)</span> 3<spanclass=′latex−bold′>(E)</span> 3 <span class='latex-bold'>(A)</span>\ 2 \qquad<span class='latex-bold'>(B)</span>\ \dfrac{3}{2} \qquad<span class='latex-bold'>(C)</span>\ \sqrt{5}-1 \qquad<span class='latex-bold'>(D)</span>\ 3 \qquad<span class='latex-bold'>(E)</span>\ \sqrt{3}
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