Áp dụng hệ quả Thalet ta có:
$\dfrac{AO}{OC}=\dfrac{OB}{OD}$ hay $\dfrac{DO}{DB}=\dfrac{OC}{AC}$
Xét $ΔABD$ có $OM//AB=>\dfrac{OM}{AB}=\dfrac{DO}{DB}$
Xét $ΔABC$ có $ON//AB=>\dfrac{ON}{AB}=\dfrac{CO}{CA}$
$=>\dfrac{OM}{AB}=\dfrac{ON}{AB}$
$=>OM=ON$. (đpcm)