Question 184
Let $ABC$ be an acute-angled triangle with $BC \gt AB$, such that the points $A$, $H$, $I$ and $C$ are concyclic (where $H$ is the orthocenter and $I$ is the incenter of triangle $ABC$). The line $AC$ intersects the circumcircle of triangle $BHC$ at point $T$, and the line $BC$ intersects the circumcircle of triangle $AHC$ at point $P$. If the lines $PT$ and $HI$ are parallel, determine the measures of the angles of triangle $ABC$.
Adrian Bud
Adrian Bud