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Interesting conditional geo in orthocentre configuration

Source: India EGMO TST 2024/6

December 31, 2023
geometryEgmo tst

Problem Statement

Let ABCABC be an acute angled triangle with orthocentre HH. Let E=BH∩ACE = BH \cap AC and F=CH∩ABF= CH \cap AB. Let D,M,ND, M, N denote the midpoints of segments AH,BD,CDAH, BD, CD respectively, and T=FM∩ENT = FM \cap EN. Suppose D,E,T,FD, E, T, F are concylic. Prove that DTDT passes through the circumcentre of ABCABC.
Proposed by Pranjal Srivastava
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