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Turkish NMO First Round - 2012 Problem - 05 {Geometry}

Source:

July 1, 2012
geometryinradius

Problem Statement

△ABC\triangle ABC is given with ∣AB∣=7,∣BC∣=12|AB|=7, |BC|=12, and ∣CA∣=13|CA|=13. Let DD be a point on [BC][BC] such that ∣BD∣=5|BD|=5. Let r1r_1 and r2r_2 be the inradii of △ABD\triangle ABD and △ACD\triangle ACD, respectively. What is r1/r2r_1/r_2?
<spanclass=′latex−bold′>(A)</span> 1<spanclass=′latex−bold′>(B)</span> 1312<spanclass=′latex−bold′>(C)</span> 75<spanclass=′latex−bold′>(D)</span> 32<spanclass=′latex−bold′>(E)</span> None <span class='latex-bold'>(A)</span>\ 1 \qquad <span class='latex-bold'>(B)</span>\ \frac{13}{12} \qquad <span class='latex-bold'>(C)</span>\ \frac{7}{5} \qquad <span class='latex-bold'>(D)</span>\ \frac{3}{2} \qquad <span class='latex-bold'>(E)</span>\ \text{None}
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