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point lies on perp. bisector wanted, intersecting circles given

Source: Norwegian Mathematical Olympiad 1995 - Abel Competition p2b

February 11, 2020
intersecting circlescirclesequal circlesperpendicular bisector

Problem Statement

Two circles of the same radii intersect in two distinct points PP and QQ. A line passing through PP, not touching any of the circles, intersects the circles again at AA and BB. Prove that QQ lies on the perpendicular bisector of ABAB.
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