27.？ BM+CN=MN？ Proof: As shown in the figure, extend AC to M 1, make CM 1 = BM, and connect DM 1:∠ABC =∠ACB = 60 according to the known conditions. ∠ DBC = ∠ DCB = 30 ∴. ∴ RT△ BDM ≌ RT△ CDM1∴ MDB = ∠ m1dcdm = DM/kloc- CN-BM = Mn Proof: As shown in the figure, cut on CN to make CM 1 = BM and connect DM 1? ∠∠ABC =∠ACB = 60，∠DBC =∠dcb = 30 ∴∠dbm=∠dcm 1=90 ∵bd=cd∴rt△bdm≌rt△cdm 1∴∠mdb=∠m 1dc？ DM=DM 1？ ∵∠bdm+∠bdn = 60 ∴∠cdm 1+∠bdn=60 ∴∠ndm 1=∠bdc-(∠m 1dc+∠bdn)= 120-60 = 60 ∴∠m 1dn=∠mdn？ ∵ad=ad∴△mdn≌△m 1dn∴mn=nm 1=nc-cm 1=nc-mb