Because BM bisects the angle ABC
So angle ABM= angle EBM
Because AM is perpendicular to BM
So AMB angle = EMB angle =90 degrees.
Because BM=BM
So right triangle ABM and right triangle EBM are congruent (ASA).
So AM=EM
AB=BE=BC+CE
Because n is the midpoint of AC
So MN is the center line of triangle ACE.
So MN= 1/2CE
Because AB=65438+ 00 BC = 6.
So CE=4
So MN=2