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Bisector, orthogonal projection

Source: 69 Polish MO 2018 Second Round - Problem 3

April 28, 2018
geometryPlane GeometrybisectorPolandcircumcircle

Problem Statement

Bisector of side BCBC intersects circumcircle of triangle ABCABC in points PP and QQ. Points AA and PP lie on the same side of line BCBC. Point RR is an orthogonal projection of point PP on line ACAC. Point SS is middle of line segment AQAQ. Show that points A,B,R,SA, B, R, S lie on one circle.
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