如图,DE‖BC,分别交AB,AC于点D,E,CD,BE相交于点O.若△DOB的面积:△COB的面积=4:9,求AE/AC

问题描述:

如图,DE‖BC,分别交AB,AC于点D,E,CD,BE相交于点O.若△DOB的面积:△COB的面积=4:9,求AE/AC

∵△DOB的面积:△COB的面积=4:9,∴OD:OC=4:9
∵DE‖BC,∴△ODE∽△OCB.∴DE:BC=OD:OC=4:9
又△ADE∽△ABC,∴AE:AC=DE:BC=4:9

图在哪?

∵△DOB的面积:△COB的面积=4:9,∴OD:OC=4:9(两个三角形等高)
∵DE‖BC,∴△ODE∽△OCB.∴DE:BC=OD:OC=4:9
又△ADE∽△ABC,∴AE:AC=DE:BC=4:9