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AP ,BQ,CR are concurrent

Source: MEMO 2018 I3

September 3, 2018
geometryptolemy sinus lemma

Problem Statement

Let ABCABC be an acute-angled triangle with AB<AC,AB<AC, and let DD be the foot of its altitude fromA.A. Let RR and QQ be the centroids of triangles ABDABD and ACDACD, respectively. Let PP be a point on the line segment BCBC such that P≠DP \neq D and points PP QQ RR and DD are concyclic .Prove that the lines APAP BQBQ and CRCR are concurrent.
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