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Prove the similarity

Source: INMO 1991 Problem 9

October 3, 2005
geometryincenterparallelogramrectangle

Problem Statement

Triangle ABCABC has an incenter II l its incircle touches the side BCBC at TT. The line through TT parallel to IAIA meets the incircle again at SS and the tangent to the incircle at SS meets AB,ACAB , AC at points C′,B′C' , B' respectively. Prove that triangle AB′C′AB'C' is similar to triangle ABCABC.
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