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prove that circles pass through a fixed point

Source: 239 2017 J2

May 31, 2020
geometrycoaxial circlesInversion

Problem Statement

Inside the circle ω\omega through points A,BA, B point CC is chosen. An arbitrary point XX is selected on the segment BCBC. The ray AXAX cuts the circle in YY. Prove that all circles CXYCXY pass through a two fixed points that is they intersect and are coaxial, independent of the position of XX.
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