取△DCE外心F,连接AF,BF,CF,DF,EF,在AC上取点G使AG=AD,连接GF,∠EFC=2∠EDC=60⁰,EF=CF,∴正△EFC,∴∠ECF=60⁰,∴∠ACF=∠ACB-∠ECF=60⁰,∴CF平分∠ACB,又CF=DF,BC=BD,∴△BCF≌△△BDF,∴∠CBF=∠DBF,,∴BF平分∠ABC,F为△ABC内心,AF平分∠BAC,又AD=AG,∴△ADF≌△AGF,∴AG=AD=8,∴GF=DF=FC,∴正△CGF,CG=CF=CE=2,∴AC=AG+GC=10,设BC=BD=x,由余弦定理(或者再作BH丄AC这样可以避免使用余弦定理),AB²=AC²+BC²-2AC·BCcos∠ACB,∴(x+8)²=10²+x²-20x·(-1/2),∴x=6,∴BE=BC-CE=4
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