问题
选择题
已知△ABC,点H,O为△ABC所在平面内的点,且
|
答案
∵
•AH
=AB
•AH
,∴( AC
-AB
)•AC
=0AH
即
•CB
=0AH
又
+OA
+OB
=OC
,∴OH
+OB
=OC
-OH
,即OA
=AH
+OB
,OC
∴
•(CB
+OB
)=0,即(OC
-OB
)•(OC
+OB
)=0,OC
∴|
|2=|OB
|2,∴OB=OBOC
同理OA=OC,
∴O是△ABC的垂心.
故选B.