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incircles in triangles of isosceles trapezoid lead to perpendicularity

Source: 2017 Oral Moscow Geometry Olympiad grades 8-9 p2

July 26, 2019
geometrytrapezoidisoscelesperpendicularincircle

Problem Statement

An isosceles trapezoid ABCDABCD with bases BCBC and ADAD is given. Circles with centers O1O_1 and O2O_2 are inscribed in triangles ABCABC and ABDABD. Prove that line O1O2O_1O_2 is perpendicular on BCBC.
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