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Turkey NMO 2010 1st Round - P33 (Geometry)

Source:

July 26, 2012
geometry

Problem Statement

Let DD be the midpoint of [AC][AC] of △ABC\triangle ABC with m(ABC^)=90∘m(\widehat{ABC})=90^\circ and ∣AC∣=10|AC|=10. Let EE be the point of intersections of bisectors of [AD][AD] and [BD][BD]. Let FF be the point of intersections of bisectors of [BD][BD] and [CD][CD]. If ∣EF∣=13|EF|=13, then ∣AB∣|AB| can be
<spanclass=′latex−bold′>(A)</span> 20213<spanclass=′latex−bold′>(B)</span> 15213<spanclass=′latex−bold′>(C)</span> 10213<spanclass=′latex−bold′>(D)</span> 5213<spanclass=′latex−bold′>(E)</span> None <span class='latex-bold'>(A)</span>\ 20\sqrt{\frac 2{13}} \qquad<span class='latex-bold'>(B)</span>\ 15\sqrt{\frac 2{13}} \qquad<span class='latex-bold'>(C)</span>\ 10\sqrt{\frac 2{13}} \qquad<span class='latex-bold'>(D)</span>\ 5\sqrt{\frac 2{13}} \qquad<span class='latex-bold'>(E)</span>\ \text{None}
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