Question 58
The segment $BC$ is fixed in the plane. Let $A$ be a point, such that $\triangle ABC$ is acute. Let $BP$ ($P \in AC$) and $CQ$ ($Q \in AB$) be altitudes in $\triangle ABC$ and $O$ is the center of the circumscribed circle about $ABC$. The points $K$ and $L$ are symmetric to $O$ with respect to the lines $AB$ and $AC$ respectively. The lines through $P$ and $Q$, orthogonal to $LP$ and $KQ$ respectively, meet at $T$. Prove that when $A$ varies, the point $T$ lies on a fixed line.
(Aleksander Ivanov)
(Aleksander Ivanov)