MathDB

33

Part of 2013 National Olympiad First Round

Problems(1)

P33 [Geometry] - Turkish NMO 1st Round - 2013

Source:

4/16/2013
Let DD be a point on side [BC][BC] of triangle ABCABC such that [AD][AD] is an angle bisector, ∣BD∣=4|BD|=4, and ∣DC∣=3|DC|=3. Let EE be a point on side [AB][AB] and different than AA such that m(BED^)=m(DEC^)m(\widehat{BED})=m(\widehat{DEC}). If the perpendicular bisector of segment [AE][AE] meets the line BCBC at MM, what is ∣CM∣|CM|?
<spanclass=′latex−bold′>(A)</span> 12<spanclass=′latex−bold′>(B)</span> 9<spanclass=′latex−bold′>(C)</span> 7<spanclass=′latex−bold′>(D)</span> 5<spanclass=′latex−bold′>(E)</span>  None of above <span class='latex-bold'>(A)</span>\ 12 \qquad<span class='latex-bold'>(B)</span>\ 9 \qquad<span class='latex-bold'>(C)</span>\ 7 \qquad<span class='latex-bold'>(D)</span>\ 5 \qquad<span class='latex-bold'>(E)</span>\ \text { None of above}
geometryangle bisectorperpendicular bisector