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2 lines concurrent on the circumcircle

Source: Romania 2017 IMO TST 2, problem 1

March 18, 2018
geometrycircumcircle

Problem Statement

Let ABCABC be a triangle with AB<ACAB<AC, let G,HG,H be its centroid and otrhocenter. Let DD be the otrhogonal projection of AA on the line BCBC, and let MM be the midpoint of the side BCBC. The circumcircle of ABCABC crosses the ray HMHM emanating from MM at PP and the ray DGDG emanating from DD at QQ, outside the segment DGDG. Show that the lines DPDP and MQMQ meet on the circumcircle of ABCABC.
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