问题 选择题
设O为△ABC的外心,且
OA
+
OB
+
2
OC
=
0
,则△ABC的内角C=(  )
A.
π
6
B.
π
4
C.
π
3
D.
π
2
答案

设外接圆的半径为R,

OA
+
OB
+
2
OC
=
0

OA
+
OB
=-
2
OC

(

OA
+
OB
) 2=(
2
OC
) 2

∴2R2+2

OA
OB
=2R2

OA
OB
=0,

∠AOB=

π
4

根据圆心角等于同弧所对的圆周的两倍得:

△ABC中的内角C值为=

π
4

故选B.

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