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Geometrical inequality

Source: Tuymaada 2017 Junior Level

July 17, 2017
geometryinequalities

Problem Statement

ABCDABCD is a cyclic quadrilateral such that the diagonals ACAC and BDBD are perpendicular and their intersection is PP . Point QQ on the segment CPCP is such that CQ=APCQ=AP . Prove that the perimeter of triangle BDQBDQ is at least 2AC2AC .
Tuymaada 2017 Q2 Juniors
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