问题 选择题
已知△ABC,点H,O为△ABC所在平面内的点,且
AH
AB
=
AH
AC
BH
BA
=
BH
BC
OA
+
OB
+
OC
=
OH
,则点O为△ABC的(  )
A.内心B.外心C.重心D.垂心
答案

AH
AB
=
AH
AC
,∴(
AB
-
AC
)•
AH
=0

CB
AH
=0

OA
+
OB
+
OC
=
OH
,∴
OB
+
OC
=
OH
-
OA
,即
AH
=
OB
+
OC

CB
•(
OB
+
OC
)=0,即(
OB
-
OC
)•(
OB
+
OC
)=0,

|

OB
|2=|
OC
|2
,∴OB=OB

同理OA=OC,

∴O是△ABC的垂心.

故选B.

单项选择题
单项选择题