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P01 [Geometry] - Turkish NMO 1st Round - 2013

Source:

April 16, 2013
geometryincenterangle bisector

Problem Statement

Let ABCABC be a triangle with incenter II, centroid GG, and ∣AC∣>∣AB∣|AC|>|AB|. If IG∥BCIG\parallel BC, ∣BC∣=2|BC|=2, and Area(ABC)=35/8Area(ABC)=3\sqrt 5 / 8, then what is ∣AB∣|AB|?
<spanclass=′latex−bold′>(A)</span> 98<spanclass=′latex−bold′>(B)</span> 118<spanclass=′latex−bold′>(C)</span> 138<spanclass=′latex−bold′>(D)</span> 158<spanclass=′latex−bold′>(E)</span> 178 <span class='latex-bold'>(A)</span>\ \dfrac 98 \qquad<span class='latex-bold'>(B)</span>\ \dfrac {11}8 \qquad<span class='latex-bold'>(C)</span>\ \dfrac {13}8 \qquad<span class='latex-bold'>(D)</span>\ \dfrac {15}8 \qquad<span class='latex-bold'>(E)</span>\ \dfrac {17}8
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