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Prove that two tangents intersect on BC

Source: Latvian TST for Baltic Way 2022 P11

November 25, 2022
geometrycircumcircle

Problem Statement

Let △ABC\triangle ABC be an acute triangle. Point DD is arbitrarily chosen on the side BCBC. Let the circumcircle of the triangle △ADB\triangle ADB intersect the segment ACAC at MM, and the circumcircle of the triangle △ADC\triangle ADC intersect the segment ABAB at NN. Prove that the tangents of the circumcircle of the triangle △AMN\triangle AMN at MM and NN intersect at a point that lies on the line BCBC.
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