Let $ABC$ be a triangle with an obtuse angle $A$ and incentre $I$. Circles $ABI$ and $ACI$ intersect $BC$ again at $X$ and $Y$ respectively. The lines $AX$ and $BI$ meet at $P$, and the lines $AY$ and $CI$ meet at $Q$. Prove that $BCQP$ is cyclic.
I drew the diagram and saw that angle $AIB$ is equal to angle $AXB$
And angle $AIC$ is equal to angle $AYC$.
I tried making such pairs for the circle $BCQP$ but couldn't do so.
I tried using angle bisector and making some triangles congruent or similar but couldn't conclude.