Question 72
In the plane, $ABC$ is an acute triangle with circumcentre $O$ and circumcircle $\Omega$. Points $D$ and $E$ are chosen on segments $AB$ and $AC$, respectively, and $\ell$ is the line through $A$ perpendicular to $DE$. Let $\ell$ meet the circumcircle of triangle $ADE$ and $\Omega$ again at $P$ and $Q$, respectively. Let the line $OQ$ meet $BC$ at $N$, let the line $OP$ meet $DE$ at $S$, and let $W$ be the orthocentre of triangle $AOS$.
Prove that the four points $S, N, O, W$ are concyclic.
Prove that the four points $S, N, O, W$ are concyclic.