# Angling-Triangling!

Geometry Level 4

Given $$\triangle ABC$$, let $$D$$ be a point on $$AB$$ produced beyond $$B$$, such that $$BD=BC$$, and let $$E$$ be a point on $$AC$$ produced beyond $$C$$, such that $$CE=BC$$. Let $$P$$ be the intersection of $$BE$$ and $$CD$$, and suppose that:

$\large{\dfrac{DP}{BE}+ \dfrac{EP}{CD} = 2\sin \left( \dfrac{\angle BAC}{2} \right) }$

Submit the value of $$\angle BAC$$ in degrees as your answer.

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