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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