Question 24
Circles $w_1$ and $w_2$ centered at points $O_1$ and $O_2$ respectively intersect at points $A$ and $B$. Let $w$ be the circumscribed circle of $O_1O_2B$ centered at $O$, which intersects $w_1$ and $w_2$ again at points $K$ and $L$ respectively. The straight line $OA$ intersects $w_1$ and $w_2$ at points $M$ and $N$ respectively. Denote by $P$ the intersection point of lines $MK$ and $NL$. Prove that $P$ lies on $w$ and $PM = PN$.
(Vadym Mytrofanov)
(Vadym Mytrofanov)