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tangency of moving nine point circle

Source: Sharygin 2023 - P7 (Grade-8-9)

March 4, 2023
geometryNine Point Circletangent circlesSharygin Geometry OlympiadSharygin 2023

Problem Statement

Let AA be a fixed point of a circle ω\omega. Let BCBC be an arbitrary chord of ω\omega passing through a fixed point PP. Prove that the nine-points circles of triangles ABCABC touch some fixed circle not depending on BCBC.
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