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Geometry about a well-known lemma

Source: Serbia JBMO TST 2024 P4

May 25, 2024
geometry

Problem Statement

Let II be the incenter of a triangle ABCABC with AB≠ACAB \neq AC. Let MM be the midpoint of BCBC, M′∈BCM' \in BC be such that IM′=IMIM'=IM and KK be the midpoint of the arc BACBAC. If AK∩BC=LAK \cap BC=L, show that KLIM′KLIM' is cyclic.
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