So BM=MC

And because MF and I share the angle AMB and the angle AMC.

So angle BME= angle EMA

Angle AMF= angle FMC

In triangle BAM and triangle CMA

AM=AM

Angle BMA= angle AMB

BM=MC

So triangle BAM is equal to triangle CMA(SAS)

So angle B= angle C.

In triangle boundary element method and triangle MFC

Angle B= angle c

BM=CM

Angle BME= angle FMC

So the triangle BEM is equal to the triangle FMC(ASA).

So BE=FC

EM=FM

So these two angles are isosceles triangles.

So EM+MF=BE+FC

According to the triangle formula, the sum of two sides is greater than the third side.

So em+MF > ef

That is, be+fc > ef.