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Geometry Mathley 1.3 collinear

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June 6, 2020
geometrycollinearincenterorthocenter

Problem Statement

Let ABCABC be an acute triangle with incenter OO, orthocenter HH, altitude AD.AOAD. AO meets BCBC at EE. Line through DD parallel to OHOH meet AB,ACAB,AC at M,NM,N, respectively. Let II be the midpoint of AEAE, and DIDI intersect AB,ACAB,AC at P,QP,Q respectively. MQMQ meets NPNP at TT. Prove that D,O,TD,O, T are collinear.
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