MathNet 2017-part-03 — 176 problems (EN–VI) Question 5

Let $ABC$ be a triangle and $O$ the centre of its circumcircle. Let $P$ be a point on $(AO)$ and $D, E, F$ the orthogonal projections of $P$ onto $(AB)$, $(BC)$ and $(CA)$. Let $X$ and $Y$ be the intersections of the circumcircles of $DEF$ and of $BCP$.

Prove that $\widehat{BAX} = \widehat{YAC}$.