Question 12
Let $ABC$ be an acute-angled triangle with $AB \lt AC$, and let $O, H$ be its circumcentre and orthocentre respectively. Points $Z, Y$ lie on segments $AB, AC$ respectively, such that
$$
\angle ZOB = \angle YOC = 90^\circ.
$$
The perpendicular line from $H$ to line $YZ$ meets lines $BO$ and $CO$ at $Q, R$ respectively. Let the tangents to the circumcircle of $\triangle AYZ$ at points $Y$ and $Z$ meet at point $T$. Prove that $Q, R, O, T$ are concyclic.
$$
\angle ZOB = \angle YOC = 90^\circ.
$$
The perpendicular line from $H$ to line $YZ$ meets lines $BO$ and $CO$ at $Q, R$ respectively. Let the tangents to the circumcircle of $\triangle AYZ$ at points $Y$ and $Z$ meet at point $T$. Prove that $Q, R, O, T$ are concyclic.