[tex]\it [AD] \equiv [BC] \Longrightarrow AD=BC\ \ \ \ (1)\\ \\ Th. \ bisectoarei\ AE \Rightarrow \dfrac{EB}{ED} =\dfrac{AB}{AD}\ \ \ \ (2)\\ \\ \\ Th. \ bisectoarei\ BF \Rightarrow \dfrac{FA}{FC} =\dfrac{AB}{BC} \stackrel{(1)}{\Longrightarrow}\ \dfrac{FA}{FC} =\dfrac{AB}{AD} \ \ \ (3)\\ \\ \\ (2),(3)\Rightarrow \dfrac{EB}{ED} =\dfrac{FA}{FC}\Rightarrow EB\cdot FC=FA\cdot ED \ \ [q.\ e.\ d.][/tex]
