MathNet 2023-part-02 — 191 problems (EN–VI) Question 12

Let $ABC$ be an acute triangle (all of whose angles are acute) with $BA \neq BC$. Let $O$ be the centre of its circumcircle. The line $(AB)$ meets the circumcircle of $BOC$ a second time at $P \neq B$. Show that $PA = PC$.