Prove two angles equal in billiard scenario.
Since $ABC\sim FEC$ we have $${AB\over EF} = {AC\over FC}$$ and since $ACD\sim AFE$ we have $${EF\over DC} = {AF\over AC}$$ So we have $${AB\over DC} ={AF\over FC}\implies AFB\sim CFD$$ and thus a conclusion.