In ΔAOB, OD is the bisector of ∠AOB.
∴ OA/OB = AD/DB ... (1)
In ΔBOC, OE is the bisector of ∠BOC
∴ OB/OC = BE/EC … (2)
In ΔCOA, OF is the bisector of ∠COA.
∴ OC/OA = CF/FA … (3)
Multiplying the corresponding sides of (1), (2) and (3), we get
⇒ DB x EC x FA = AD x BE x CF
Hence proved.