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circumcenter of triangle of projections of P on sides of ABC is interior point

Source: Sharygin 2006 finals 8.6

September 10, 2019
geometrycircumcircleCircumcenterinteriorprojections

Problem Statement

A triangle ABCABC and a point PP inside it are given. A′,B′,C′A', B', C' are the projections of PP onto the straight lines ot the sides BC,CA,ABBC,CA,AB. Prove that the center of the circle circumscribed around the triangle A′B′C′A'B'C' lies inside the triangle ABCABC.
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