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2

Part of 2018 Federal Competition For Advanced Students, P2

Problems(1)

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

5/25/2019
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)
geometric inequalitygeometrycyclic quadrilateral