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Incircle of a triangle is tangent to (ABC)

Source: XVII Sharygin Correspondence Round P18

March 2, 2021
geometrycircumcircle

Problem Statement

Let ABCABC be a scalene triangle, AMAM be the median through AA, and ω\omega be the incircle. Let ω\omega touch BCBC at point TT and segment ATAT meet ω\omega for the second time at point SS. Let δ\delta be the triangle formed by lines AMAM and BCBC and the tangent to ω\omega at SS. Prove that the incircle of triangle δ\delta is tangent to the circumcircle of triangle ABCABC.
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