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rectangle with vertices on sides of triangle

Source: Sharygin Final 2024 8.5

August 2, 2024
geometryrectangleSharygin Geometry OlympiadSharygin 2024

Problem Statement

The vertices MM, NN, KK of rectangle KLMNKLMN lie on the sides ABAB, BCBC, CACA respectively of a regular triangle ABCABC in such a way that AM=2AM = 2, KC=1KC = 1. The vertex LL lies outside the triangle. Find the value of ∠KMN\angle KMN.
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