问题 选择题
在梯形ABCD中,
AB
=2
DC
,AC与BD相交于O点.若
AB
=
a
AD
=
b
,则
OC
=(  )
A.
1
6
a
+
1
3
b
B.
1
2
a
-
1
4
b
C.
1
3
a
+
1
6
b
D.
1
6
a
-
1
3
b
答案

由题意可得AB=2CD.

由△AOB△COD 可得

1
2
=
CD
AB
=
OC
OA

∴AO=

2
3
AC,
OC
=
1
3
AC
=
1
3
AD
+
DC

=

1
3
AD
+
1
2
AB
)=
1
6
AB
+
1
3
AD

=

1
6
a
+
1
3
b

故选A

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