# Triangles

Geometry Level 4

In a triangle $$ABC$$, $$\angle BAC=15^\circ$$ and length $$AB$$ is 10. Point $$D$$ is the point of intersection of the perpendicular bisectors of $$AB$$ and $$BC$$. Given that length $$CD$$ is 8, find the perimeter $$P$$ of the quadrilateral $$ABCD$$.

Input your answer as $$\left\lfloor 1000P \right\rfloor$$.

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