Problem

Source: Tuymaada 2017 Junior Level

Tags: geometry, inequalities



$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