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An acute triangle

Source: 2016 Ukraine TST

May 13, 2018
geometryincirclecircumcircleparallelTSTincenter

Problem Statement

Let ABCABC be an acute triangle with AB<BCAB<BC. Let II be the incenter of ABCABC, and let ω\omega be the circumcircle of ABCABC. The incircle of ABCABC is tangent to the side BCBC at KK. The line AKAK meets ω\omega again at TT. Let MM be the midpoint of the side BCBC, and let NN be the midpoint of the arc BACBAC of ω\omega. The segment NTNT intersects the circumcircle of BICBIC at PP. Prove that PM∥AKPM\parallel AK.
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