Binzhou m hotel

Solution: the connection BE and AD intersect at point m, then BE is the minimum value of EM+CM.

Take the midpoint f of CE and connect df.

∵ equilateral △ABC's side length is 6, AE=2,

∴CE=AC-AE=6-2=4，

∴CF=EF=AE=2，

And ∵AD is the center line on the side of BC,

∴DF is the center line of △BCE,

∴BE=2DF,BE∥DF，

And ∵E is the midpoint of AF,

∴M is the midpoint of AD,

∴ME is the center line of△ △ADF,

∴DF=2ME，

∴BE=2DF=4ME，

∴BM=BE-ME=4ME-ME=3ME，

∴BE=43BM.

In the right angle △BDM, BD= 12BC=3, DM= 12AD=332.

∴BM=BD2+DM2=327，

∴BE=43×327=27.

∫EM+CM = BE

The minimum value of em+cm is 27.