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2019 Saint Petersburg MO Grade 11 P4

Source: 2019 Saint Petersburg

April 14, 2019
geometryperimeter

Problem Statement

A non-equilateral triangle △ABC\triangle ABC of perimeter 1212 is inscribed in circle ω\omega .Points PP and QQ are arc midpoints of arcs ABCABC and ACBACB , respectively. Tangent to ω\omega at AA intersects line PQPQ at RR. It turns out that the midpoint of segment ARAR lies on line BCBC . Find the length of the segment BCBC.
(А. Кузнецов)
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