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<AST = 90^o wanted, incircle and altitude related

Source: 2017 Latvia BW TST P10

December 16, 2022
geometryright angleincircle

Problem Statement

In an obtuse triangle ABCABC, for which AC<ABAC < AB, the radius of the inscribed circle is RR, the midpoint of its arc BCBC (which does not contain AA) is SS. A point TT is placed on the extension of altitude ADAD such that DD is between A A and TT and AT=2RAT = 2R. Prove that ∠AST=90o\angle AST = 90^o.
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