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P05 [Geometry] - Turkish NMO 1st Round - 2014

Source:

May 21, 2014
geometry

Problem Statement

Let DD be a point on side [BC][BC] of △ABC\triangle ABC such that ∣AB∣=∣AC∣|AB|=|AC|, ∣BD∣=6|BD|=6 and ∣DC∣=10|DC|=10. If the incircles of △ABD\triangle ABD and △ADC\triangle ADC touch side [AD][AD] at EE and FF, respectively, what is∣EF∣|EF|?
<spanclass=′latex−bold′>(A)</span> 12<spanclass=′latex−bold′>(B)</span> 23<spanclass=′latex−bold′>(C)</span> 1<spanclass=′latex−bold′>(D)</span> 98<spanclass=′latex−bold′>(E)</span> 2 <span class='latex-bold'>(A)</span>\ \dfrac{1}{\sqrt{2}} \qquad<span class='latex-bold'>(B)</span>\ \dfrac{2}{\sqrt{3}} \qquad<span class='latex-bold'>(C)</span>\ 1 \qquad<span class='latex-bold'>(D)</span>\ \dfrac{9}{8} \qquad<span class='latex-bold'>(E)</span>\ 2
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