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concyclicity squashed by projections

Source: Sharygin 2023 - P1 (Grade-8)

March 4, 2023
geometryConcyclicSharygin Geometry OlympiadSharygin 2023

Problem Statement

Let LL be the midpoint of the minor arc ACAC of the circumcircle of an acute-angled triangle ABCABC. A point PP is the projection of BB to the tangent at LL to the circumcircle. Prove that PP, LL, and the midpoints of sides ABAB, BCBC are concyclic.
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