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Sharygin CR 2019 P15

Source: Sharygin CR 2019 P15 (Grade 9 - 11)

March 6, 2019
geometry

Problem Statement

The incircle ω\omega of triangle ABCABC touches the sides BCBC, CACA and ABAB at points DD, EE and FF respectively. The perpendicular from EE to DFDF meets BCBC at point XX, and the perpendicular from FF to DEDE meets BCBC at point YY. The segment ADAD meets ω\omega for the second time at point ZZ. Prove that the circumcircle of the triangle XYZXYZ touches ω\omega.
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