S△AMC=S△AMB，S△OMC=S△OMB
So S△AOC=S△AOB
AE/EB=S△ACE/S△BCE=S△AOE/S△BOE
So AE/EB=S△AOC/S△BOC.
In the same way; In a similar way
So AD/CD=S△AOB/S△BOC
So ad/CD = s △ AOB/s △ BOC = s △ AOC/s △ BOC = AE/EB.
So ED//BC
You can also use the inverse theorem of Seva's theorem.