# A problem by minimario minimario

Level pending

Right triangle $$ABC$$ with right angle at $$B$$ has $$\angle BAC=50^\circ$$ and $$\angle ACB=40^\circ$$. Points $$D, E$$ lie on side $$BC$$ such that $$DE=9000 \text{ cm}, \angle DAE=10^\circ$$ and $$\angle BAD=\angle EAC$$. The ratio $$\frac{DB}{CE}$$ can be expressed in the form $$\frac{m}{n}$$, where $$m$$ and $$n$$ are relatively prime positive integers. Find $$m+n$$.

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