如图所示.梯形ABCD中,AD∥BC,BD,AC交于O点,过O的直线分别交AB,CD于E,F,且EF∥BC.AD=12厘米,BC=20厘米.求EF.

问题描述:

如图所示.梯形ABCD中,AD∥BC,BD,AC交于O点,过O的直线分别交AB,CD于E,F,且EF∥BC.AD=12厘米,BC=20厘米.求EF.

∵AD∥BC,EF∥BC,

AD
BC
=
OA
OC
=
12
20
=
3
5

OE
BC
=
OA
AC
=
3
8
OF
AD
=
OC
AD
=
5
8

∴OE=
3
8
BC=
15
2
,OF=
5
8
AD=
15
2

∴EF=OE+OF=15.