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AB + BD > AC + CD in cyclic ABCD, AB is the longest side

Source: 49th Austrian Mathematical Olympiad National Competition (Final Round, part 2, ) 31st May 2018 p2

May 25, 2019
geometric inequalitygeometrycyclic quadrilateral

Problem Statement

Let A,B,CA, B, C and DD be four different points lying on a common circle in this order. Assume that the line segment ABAB is the (only) longest side of the inscribed quadrilateral ABCDABCD. Prove that the inequality AB+BD>AC+CDAB + BD > AC + CD holds.
(Proposed by Karl Czakler)