问题
选择题
设G是△ABC的重心,且(sinA)•
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答案
∵G是三角形ABC的重心,∴
+GA
+GB
=GC
,0
则
=-GA
-GB
,代入(sinA)•GC
+(sinB)•GA
+(sinC)•GB
=GC
得,0
(sinB-sinA)
++(sinC-sinA)GB
=GC
,0
∵
,GB
不共线,∴sinB-sinA=0,sinC-sinA=0,GC
则sinB=sinA=sinC,根据正弦定理知:b=a=c,
∴三角形是等边三角形,则角B=60°.
故选B.