Given an obtuse triangle ABC with \(\overline{AB}\) past B to a point D such that \(\overline{CD}\) is perpendicular to \(\overline{AB}\) . Let F be the point on line segment \(\overline{AC}\) such that \(\overline{BF}\) is perpendicular to \(\overline{AB}\) , and extend \(\overline{BF}\) past F to a point E such that \(\overline{BE}\) is perpendicular to \(\overline{CE}\). Given that \(\angle ECF = \angle BCD\), show that \(\triangle ABC \sim \triangle BFC\) .
