Question 7
Let $ABC$ be an isosceles triangle with a base $\overline{AB}$. A point $P$ is chosen on the segment $\overline{AC}$ and a point $Q$ is chosen on the segment $\overline{BC}$ such that $|AP| + |BQ| = |PQ|$. The line parallel with the line $BC$ which passes through the midpoint of the segment $\overline{PQ}$ intersects the segment $\overline{AB}$ in the point $N$. Circumcircle of the triangle $PNQ$ intersects the line $AC$ in the points $P$ and $K$, and the line $BC$ in the points $Q$ and $L$. If the point $R$ is the intersection of the lines $PL$ and $QK$, prove that the line $PQ$ is perpendicular to the line $CR$. (Stipe Vidak)