Question 162
An acute-angled triangle $ABC$ is given, such that $|AB| \gt |AC|$. Let $O$ be the centre of the circumcircle, and let $OQ$ be a diameter of the circumcircle of triangle $BOC$. The line parallel to $BC$ passing through $A$ intersects the line $CQ$ at $M$, while the line parallel to $CQ$ and passing through $A$ intersects the line $BC$ at $N$. Denote by $T$ the intersection of $AQ$ and $MN$.
Show that $T$ lies on the circumcircle of triangle $BOC$.
(Ukraine 2005)
Show that $T$ lies on the circumcircle of triangle $BOC$.
(Ukraine 2005)