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