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a bisector of an acute triangle

Source: All-Russian 2007

May 4, 2007
geometrycircumcircleAsymptotecyclic quadrilateralangle bisectorgeometry proposed

Problem Statement

BB1BB_{1} is a bisector of an acute triangle ABCABC. A perpendicular from B1B_{1} to BCBC meets a smaller arc BCBC of a circumcircle of ABCABC in a point KK. A perpendicular from BB to AKAK meets ACAC in a point LL. BB1BB_{1} meets arc ACAC in TT. Prove that KK, LL, TT are collinear. V. Astakhov
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