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Proving AH is tangent to MNH

Source: Turkey EGMO TST 2020 P1

February 6, 2020
geometrycircumcircle

Problem Statement

HH is the orthocenter of a non-isosceles acute triangle △ABC\triangle ABC. MM is the midpoint of BCBC and BB1,CC1BB_1, CC_1 are two altitudes of △ABC\triangle ABC. NN is the midpoint of B1C1B_1C_1. Prove that AHAH is tangent to the circumcircle of △MNH\triangle MNH.
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