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Geometry Mathley 13.3 concurrent iff concyclic

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June 7, 2020
concurrentConcyclicgeometrycyclic quadrilateral

Problem Statement

Let ABCDABCD be a quadrilateral inscribed in circle (O)(O). Let M,NM,N be the midpoints of AD,BCAD,BC. A line through the intersection PP of the two diagonals AC,BDAC,BD meets AD,BCAD,BC at S,TS, T respectively. Let BSBS meet ATAT at QQ. Prove that three lines AD,BC,PQAD,BC,PQ are concurrent if and only if M,S,T,NM, S, T,N are on the same circle.
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