Let $ABC$ be a triangle, and $P$ a variable point on its circumcircle. Suppose $AP$ meets $BC$ at $Q$. What is the locus of the circumcentre of $\triangle BPQ$?
Experiments on GeoGebra show that the locus is a line through $B$, but I am struggling to identify this line, or see anything geometrically significant in the diagram. Could someone help me to prove this synthetically? Thank you.