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parallel lines by projections inside a cyclic ABCD

Source: 2010 Oral Moscow Geometry Olympiad grades 10-11 p2

May 8, 2020
geometrycyclic quadrilateralperpendicularparallel

Problem Statement

Quadrangle ABCDABCD is inscribed in a circle. The perpendicular from the vertex CC on the bisector of ∠ABD\angle ABD intersects the line ABAB at the point C1C_1. The perpendicular from the vertex BB on the bisector of ∠ACD\angle ACD intersects the line CDCD at the point B1B_1. Prove that B1C1∥ADB_1C_1 \parallel AD.
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