KöMaL 2023 C1750

$M$ and $N$ are the common points of circles $k_1$, centred at $O_1$ and $k_2$, centred at $O_2$. A secant drawn through point $M$ intersects circle $k_1$ at point $A$ and circle $k_2$ at point $B$ such that $A$ lies outside circle $k_2$ and $B$ lies outside circle $k_1$. Lines $AO_1$ and $BO_2$ intersect at point $P$. Points $N$ and $P$ lie in the same half plane determined by line $O_1O_2$. Show that $P$ lies on the circumscribed circle of triangle $O_1NO_2$.