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The incircle of a triangle ABC has centre I

Source: 239MO 2004, grade 8-9, problem 2

December 11, 2004
geometryRussiabisector

Problem Statement

The incircle of a triangle ABCABC has centre II and touches sides AB,BC,CAAB, BC, CA in points C1,A1,B1C_1, A_1, B_1 respectively. Denote by LL the foot of a bissector of angle BB, and by KK the point of intersecting of lines B1IB_1I and A1C1A_1C_1. Prove that KL∥BB1KL\parallel BB_1. proposed by L. Emelyanov, S. Berlov
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