TUYMAADA 2017 Problem 2

$ABCD$ is a cyclic quadrilateral such that the diagonals $AC$ and $BD$ are perpendicular and their intersection is $P$ . Point $Q$ on the segment $CP$ is such that $CQ=AP$ . Prove that the perimeter of triangle $BDQ$ is at least $2AC$ .

Tuymaada 2017 Q2 Juniors