Question 170
Five points $A$, $B$, $C$, $D$, $P$ lie on a plane. Points $A$, $B$, $C$, $D$ lie on a straight line in this order. Furthermore, it is known that $AB = BC = CD = 6$, $PB = 5$ and $PC = 7$ are satisfied. Here we denote the length of the line segment $XY$ also by $XY$. Let $Q$ be the point of intersection, different from $P$, of the circumcircle of the triangle $PAC$ and the circumcircle of the triangle $PBD$. Determine the length of the line segment $PQ$.