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(2014•郑州二模)如图所示,点A,B,C是圆O上的三点,线段OC与线段AB交于圆内一点P,若OC=mOA+2mOB,AP=λAB,则λ=()A.56B.45C.34D.23

题目详情
(2014•郑州二模)如图所示,点A,B,C是圆O上的三点,线段OC与线段AB交于圆内一点P,若
OC
=m
OA
+2m
OB
AP
AB
,则λ=(  )

A.
5
6

B.
4
5

C.
3
4

D.
2
3
▼优质解答
答案和解析
AP
OP
OA
,∵
OP
OC
共线,∴存在实数μ,使:
OP
=μ
OC
=mμ
OA
+2mμ
OB

AP
=mμ
OA
+2mμ
OB
OA
=(mμ−1)
OA
+2mμ
OB
=−λ
OA
OB

mμ−1=−λ
2mμ=λ
解得λ=
2
3

故选D.