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Coaxial Circles and moving hypotenuse

Source: Saint Petersburg MO 2016

December 11, 2016
geometrycircumcirclePower of Pointcoaxial circles

Problem Statement

Points AA and PP are marked in the plane not lying on the line \ell. For all right triangles ABCABC with hypotenuse on \ell, show that the circumcircle of triangle BPCBPC passes through a fixed point other than PP.