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// wanted, circumcircle, equal segments, perp (Ukr. Geom. Olympiad '20 VIII p3)

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June 8, 2020
geometrycircumcircleparallelperpendicularequal segments

Problem Statement

Triangle ABCABC. Let B1B_1 and C1C_1 be such points, that AB=BB1,AC=CC1AB= BB_1, AC=CC_1 and B1,C1B_1, C_1 lie on the circumscribed circle Γ\Gamma of △ABC\vartriangle ABC. Perpendiculars drawn from from points B1B_1 and C1C_1 on the lines ABAB and ACAC intersect Γ\Gamma at points B2B_2 and C2C_2 respectively, these points lie on smaller arcs ABAB and ACAC of circle Γ\Gamma respectively, Prove that BB2∥CC2BB_2 \parallel CC_2.
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