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P13 [Geometry] - Turkish NMO 1st Round - 2013

Source:

April 16, 2013
geometrycircumcircleincenterperpendicular bisectorangle bisector

Problem Statement

Let DD and EE be points on side [BC][BC] of a triangle ABCABC with circumcenter OO such that DD is between BB and EE, ∣AD∣=∣DB∣=6|AD|=|DB|=6, and ∣AE∣=∣EC∣=8|AE|=|EC|=8. If II is the incenter of triangle ADEADE and ∣AI∣=5|AI|=5, then what is ∣IO∣|IO|?
<spanclass=′latex−bold′>(A)</span> 295<spanclass=′latex−bold′>(B)</span> 5<spanclass=′latex−bold′>(C)</span> 235<spanclass=′latex−bold′>(D)</span> 215<spanclass=′latex−bold′>(E)</span> None of above <span class='latex-bold'>(A)</span>\ \dfrac {29}{5} \qquad<span class='latex-bold'>(B)</span>\ 5 \qquad<span class='latex-bold'>(C)</span>\ \dfrac {23}{5} \qquad<span class='latex-bold'>(D)</span>\ \dfrac {21}{5} \qquad<span class='latex-bold'>(E)</span>\ \text{None of above}
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