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# Given an obtuse triangle with obtuse, extend past to a point such that is perpendicular

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Given an obtuse triangle $$ABC$$  with $$\angle ABC$$ obtuse, extend $$\overline{AB}$$ 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 $$\triangle ABC \sim \triangle BFC$$.

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Jan 16, 2020