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American point shows in Ibero geo!

Source: Iberoamerican MO 2024 Day 1 P2

September 21, 2024
geometrycircumcircle

Problem Statement

Let △ABC\triangle ABC be an acute triangle and let M,NM, N be the midpoints of AB,ACAB, AC respectively. Given a point DD in the interior of segment BCBC with DB<DCDB<DC, let P,QP, Q the intersections of DM,DNDM, DN with AC,ABAC, AB respectively. Let R≠AR \ne A be the intersection of circumcircles of triangles △PAQ\triangle PAQ and △AMN\triangle AMN. If KK is midpoint of ARAR, prove that ∠MKN=2∠BAC\angle MKN=2\angle BAC
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