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Circumcircles eat fish

Source: 2020 ISL G7

July 20, 2021
geometrycircumcircleIMO ShortlistIMO Shortlist 2020Fish

Problem Statement

Let PP be a point on the circumcircle of acute triangle ABCABC. Let D,E,FD,E,F be the reflections of PP in the AA-midline, BB-midline, and CC-midline. Let ω\omega be the circumcircle of the triangle formed by the perpendicular bisectors of AD,BE,CFAD, BE, CF.
Show that the circumcircles of △ADP,△BEP,△CFP,\triangle ADP, \triangle BEP, \triangle CFP, and ω\omega share a common point.
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