Problem

Source: Sharygin 2006 X-XI CR 22

Tags: geometry, fixed, Circumcenter, Locus



Given points $A, B$ on a circle and a point $P$ not lying on the circle. $X$ is an arbitrary point of the circle, $Y$ is the intersection point of lines $AX$ and $BP$. Find the locus of the centers of the circles circumscribed around the triangles $PXY$.