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RMO KV 2023 P1

Source: RMO 2023 P1

October 29, 2023
geometry

Problem Statement

Given a triangle ABCABC with ∠ACB=120∘.\angle ACB = 120^{\circ}. A point LL is marked in the side ABAB such that CLCL bisects ∠ACB.\angle ACB. Points NN and KK are chosen in the sides ACAC and BCBC such that CK+CN=CL.CK+CN=CL. Prove that the triangle KLNKLN is equilateral.
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