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Prove that the angles $AMP$ and $BMN$ are equal.

Source: Moldova JTST 2023

May 5, 2023
geometrytrapezoid

Problem Statement

Let ABCDABCD be a trapezoid with bases AB AB and CDCD (AB>CD)(AB>CD). Diagonals ACAC and BDBD intersect in point N N and lines ADAD and BCBC intersect in point M M. The circumscribed circles of ADNADN and BCNBCN intersect in point P P, different from point N N. Prove that the angles AMPAMP and BMNBMN are equal.
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