Triangles

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 $\left\lfloor 1000P \right\rfloor$ .