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Geometry from legendary author

Source: Kyiv City MO 2022 Round 1, Problem 8.3

January 23, 2022
geometry

Problem Statement

In triangle ABCABC ∠B>90∘\angle B > 90^\circ. Tangents to this circle in points AA and BB meet at point PP, and the line passing through BB perpendicular to BCBC meets the line ACAC at point KK. Prove that PA=PKPA = PK.
(Proposed by Danylo Khilko)
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