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Nice Nikolai Geometry

Source: Komal A. 877

April 12, 2024
geometrycircumcircle

Problem Statement

A convex quadrilateral ABCDABCD is circumscribed about circle ω\omega. A tangent to ω\omega parallel to ACAC intersects BDBD at a point PP outside of ω\omega. The second tangent from PP to ω\omega touches ω\omega at a point TT. Prove that ω\omega and circumcircle of ATCATC are tangent.
Proposed by Nikolai Beluhov, Bulgaria
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