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easy geometry

Source: iranian TST second exam p2

June 3, 2015
geometryincentercircumcircle

Problem Statement

In triangle ABCABC(with incenter II) let the line parallel to BCBC from AA intersect circumcircle of △ABC\triangle ABC at A1A_1 let AI∩BC=DAI\cap BC=D and EE is tangency point of incircle with BCBC let EA1∩⊙(△ADE)=T EA_1\cap \odot (\triangle ADE)=T prove that AI=TIAI=TI.
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