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Inradius of triangles formed by diagonals

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April 28, 2009
geometryinradiusperimeter

Problem Statement

Let E E be the intersection of the diagonals of the convex quadrilateral ABCD ABCD. The perimeters of △AEB \triangle AEB, △BEC \triangle BEC, △CED \triangle CED, and △DEA \triangle DEA are all same. If inradii of △AEB \triangle AEB, △BEC \triangle BEC, △CED \triangle CED are 3,4,6 3,4,6, respectively, then inradius of △DEA \triangle DEA will be ?
<spanclass=′latex−bold′>(A)</span> 92<spanclass=′latex−bold′>(B)</span> 72<spanclass=′latex−bold′>(C)</span> 133<spanclass=′latex−bold′>(D)</span> 5<spanclass=′latex−bold′>(E)</span> None<span class='latex-bold'>(A)</span>\ \frac {9}{2} \qquad<span class='latex-bold'>(B)</span>\ \frac {7}{2} \qquad<span class='latex-bold'>(C)</span>\ \frac {13}{3} \qquad<span class='latex-bold'>(D)</span>\ 5 \qquad<span class='latex-bold'>(E)</span>\ \text{None}
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