Iranian Geometry Olympiad 2020 (Advanced) P2

For discussing Olympiad level Geometry Problems
IftakharTausifFarhan
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Iranian Geometry Olympiad 2020 (Advanced) P2

Unread post by IftakharTausifFarhan » Sat Dec 12, 2020 4:24 pm

Let $ABC$ be an acute-angled triangle with its incenter $I$. Suppose that $N$ is the midpoint of the arc $BAC$ of the circumcircle of triangle $ABC$, and $P$ is a point such that $ABPC$ is a parallelogram. Let $Q$ be the reflection of $A$ over $N$, and $R$ the projection of $A$ on $QI$. Show that the line $AI$ is tangent to the circumcircle of triangle $PQR$.

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