Question

help

Answer 1

Xét ΔOAB và ΔOCD có

\(\widehat{OAB}=\widehat{OCD}\)

\(\widehat{AOB}=\widehat{COD}\)

Do đó: ΔOAB đồng dạng với ΔOCD

=>\(\dfrac{OA}{OC}=\dfrac{OB}{OD}\)

=>\(\dfrac{OA}{OB}=\dfrac{OC}{OD}=\dfrac{OA+OC}{OB+OD}=\dfrac{AC}{BD}\)

=>\(\dfrac{AO}{AC}=\dfrac{BO}{BD}\)(1)

Xét ΔADC có OM//DC

nên \(\dfrac{OM}{DC}=\dfrac{AO}{AC}\)(2)

Xét ΔBDC có ON//DC

nên \(\dfrac{ON}{DC}=\dfrac{BO}{BD}\left(3\right)\)

Từ (1),(2),(3) suy ra OM=ON