Question 174
Acute-angled triangle $ABC$ is given. On the perpendicular bisectors to sides $AB$ and $BC$ respectively, points $P$ and $Q$ are chosen. Let $M$ and $N$ be the projections of $P$ and $Q$ onto $AC$ (Fig.09). It turns out, that $2MN = AC$. Prove, that circumcircle of triangle $PBQ$ passes through the circumcenter of triangle $ABC$.
Fig.09
Fig.09