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perp. bisector of AB passes through fixed point as A,B move along 2 circles

Source: Sharygin 2006 VIII-IX CR 2

August 22, 2019
geometryperpendicular bisectorcirclesequal circlesFixed pointfixed

Problem Statement

Points A,BA, B move with equal speeds along two equal circles. Prove that the perpendicular bisector of ABAB passes through a fixed point.