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locus of centers of orthogonal circles to intersecting circles

Source: Israel Grosman Memorial Mathematical Olympiad 1995 p4

February 15, 2020
circlesLocusgeometryintersecting circles

Problem Statement

Two given circles α\alpha and β\beta intersect each other at two points. Find the locus of the centers of all circles that are orthogonal to both α\alpha and β\beta.
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