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Collinear problem

Source: China South East Mathematical Olympiad 2011

August 18, 2011
geometry proposedgeometry

Problem Statement

In triangle ABCABC , AA0,BB0,CC0AA_0,BB_0,CC_0 are the angle bisectors , A0,B0,C0A_0,B_0,C_0are on sides BC,CA,AB,BC,CA,AB, draw A0A1//BB0,A0A2//CC0A_0A_1//BB_0,A_0A_2//CC_0 ,A1A_1 lies on ACAC ,A2A_2 lies on ABAB , A1A2A_1A_2 intersects BCBC at A3A_3.B3B_3 ,C3C_3 are constructed similarly.Prove that : A3,B3,C3A_3,B_3,C_3 are collinear.
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