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# Triangle $ABC$ has a right angle at $B$. Legs $\overline{AB}$ and $\overline{CB}$ are extended past point $B$ to points $D$ and $E$, respect

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Triangle $$ABC$$ has a right angle at $$B$$. Legs $$\overline{AB}$$ and $$\overline{CB}$$are extended past point $$B$$ to points $$D$$ and $$E$$, respectively, such that $$\angle EAC = \angle ACD = 90^\circ$$. Prove that $$EB \cdot BD = AB \cdot BC$$.

Guest Nov 18, 2017