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KM perpendicular to EF

Source: Own. IMO 2021 Malaysian Training Camp 2

January 30, 2021
geometry

Problem Statement

Let ABCABC be a triangle with incircle centered at II, tangent to sides ACAC and ABAB at EE and FF respectively. Let NN be the midpoint of major arc BACBAC. Let ININ intersect EFEF at KK, and MM be the midpoint of BCBC. Prove that KM⊥EFKM\perp EF.
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