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Turkey NMO 2010 1st Round - P29 (Geometry)

Source:

July 26, 2012
geometryincentertrigonometry

Problem Statement

Let II be the incenter of △ABC\triangle ABC, and OO be the excenter corresponding to BB. If ∣BI∣=12|BI|=12, ∣IO∣=18|IO|=18, and ∣BC∣=15|BC|=15, then what is ∣AB∣|AB|?
<spanclass=′latex−bold′>(A)</span> 16<spanclass=′latex−bold′>(B)</span> 18<spanclass=′latex−bold′>(C)</span> 20<spanclass=′latex−bold′>(D)</span> 22<spanclass=′latex−bold′>(E)</span> 24 <span class='latex-bold'>(A)</span>\ 16 \qquad<span class='latex-bold'>(B)</span>\ 18 \qquad<span class='latex-bold'>(C)</span>\ 20 \qquad<span class='latex-bold'>(D)</span>\ 22 \qquad<span class='latex-bold'>(E)</span>\ 24
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