如图,已知在△ABC中,点D、E分别在AB、AC上,且AD•AB=AE•AC,CD与BE相交于点O. (1)求证:△AEB∽△ADC; (2)求证:BO/CO=DO/EO.

问题描述:

如图,已知在△ABC中,点D、E分别在AB、AC上,且AD•AB=AE•AC,CD与BE相交于点O.

(1)求证:△AEB∽△ADC;
(2)求证:

BO
CO
DO
EO

证明:(1)∵AD•AB=AE•AC,

AB
AC
=
AE
AD

又∵∠EAB=∠DAC,
∴△AEB∽△ADC;
(2)∵△AEB∽△ADC;
∴∠DBO=∠ECO,
又∵∠DOB=∠EOC,
∴△BOD∽△COE,
BO
CO
DO
EO