[tex]\it [AD]\equiv[BC]\Rightarrow AD=BC\ \ \ \ (1)\\ \\ Th.\ bisectoarei\ pentru\ [AE \Rightarrow\dfrac{EB}{ED}=\dfrac{AB}{AD}\ \ \ \ (2)\\ \\ Th.\ bisectoarei\ pentru\ [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]
