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AB <AD + CD , <BAC < <DCB, < BOD = <ADC = a , ABCD cyclic

Source: 2016 Bulgaria JBMO TST 1.1

August 11, 2020
geometrygeometric inequalityanglescyclic quadrilateral

Problem Statement

The quadrilateral ABCDABCD, in which ∠BAC<∠DCB\angle BAC < \angle DCB , is inscribed in a circle cc, with center OO. If ∠BOD=∠ADC=α\angle BOD = \angle ADC = \alpha. Find out which values of α\alpha the inequality AB<AD+CDAB <AD + CD occurs.
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