Let D be a point on side [BC] of triangle ABC such that [AD] is an angle bisector, ∣BD∣=4, and ∣DC∣=3. Let E be a point on side [AB] and different than A such that m(BED)=m(DEC). If the perpendicular bisector of segment [AE] meets the line BC at M, what is ∣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