ABC is a right triangle with ∠ABC=90∘ withAB=30 sqrt 3andBC=30.Dis a point on segmentBCsuch thatADis the median.Eis a point on segmentACsuch thatBEis perpendicular toAC.ADandBEintersect atF. IfEF=(a sqrt b)/c, whereaandcare positive, coprime integers andbis not divisible by the square of any prime, what is the value ofa+b+c?