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Sharygin CR 2019 P8

Source:

March 6, 2019
geometry

Problem Statement

The circle ω1\omega_1 passes through the vertex AA of the parallelogram ABCDABCD and touches the rays CB,CDCB, CD. The circle ω2\omega_2 touches the rays AB,ADAB, AD and touches ω1\omega_1 externally at point TT. Prove that TT lies on the diagonal ACAC
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