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orthocenter of MNK is the circumcenter of the inscribed hexagon

Source: 1996 Argentina OMA L3 p3

June 11, 2020
geometrycircumcirclehexagonCircumcenterorthocenter

Problem Statement

The non-regular hexagon ABCDEFABCDEF is inscribed on a circle of center OO and AB=CD=EFAB = CD = EF. If diagonals ACAC and BDBD intersect at MM, diagonals CECE and DFDF intersect at NN, and diagonals AEAE and BFBF intersect at KK, show that the heights of triangle MNKMNK intersect at OO.
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