题目内容

△ABC内接于以O为圆心,1为半径的圆,且
OA
+2
OB
-
OC
=
0
,则
OC
AB
的值为(  )
A.-1B.1C.-2D.2
由题意,|OA|=|OB|=|OC|=1,由
OA
+2
OB
-
OC
=
0
,可得
OC
=
OA
+2
OB

∴平方可得 1=1+4
OA
OB
+4,
OA
OB
=-1.
OC
AB
=(
OA
+2
OB
)•(
OB
-
OA
)=
OA
OB
-
OA
2
+2
OB
2
-2
OA
OB
=-1-1+2+2=2,
故选:D.
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