如图,已知DE∥BC,CD和BE相交于O,若S△DOE:S△COB=9:16,则AD:DB=_.

问题描述:

如图,已知DE∥BC,CD和BE相交于O,若S△DOE:S△COB=9:16,则AD:DB=______.

∵DE∥BC,
∴△ADE∽△ABC,
∵S△DOE:S△COB=9:16,

1
2
AD•AE•sin∠BAC
1
2
AB•AC•sin∠BAC
=
9
16

AD
AB
=
3
4

∴AD:DB=3:1.