MathNet 2023-part-06 — 191 problems (EN–VI) Question 187

Let $I$ be the incenter of the triangle $ABC$, and $P$ be any point on the arc $BAC$ of the circumscribed circle. On the tangent to the circumscribed circle $\omega$ of the triangle $API$ at the point $I$ points $K$ and $L$ were selected so that $BK = KI$ and $CL = LI$. Prove that the circumcircle of the triangle $PKL$ is tangent to $\omega$.
(Mykhailo Shtandenko)


Fig. 13


Fig. 14