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Nice geo problem

Source: Romania JBMO tst 2023 day 2 p2

April 30, 2023
geometryTriangle

Problem Statement

Let ABCABC be an acute-angled triangle with BC>ABBC > AB, such that the points AA, HH, II and CC are concyclic (where HH is the orthocenter and II is the incenter of triangle ABCABC). The line ACAC intersects the circumcircle of triangle BHCBHC at point TT, and the line BCBC intersects the circumcircle of triangle AHCAHC at point PP. If the lines PTPT and HIHI are parallel, determine the measures of the angles of triangle ABCABC.
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