ABCD is a convex quadrilateral with diagonals AC and BD intersecting at X. The circumcircles of the triangles AXB, BXC, CXD and DXA have centres P, Q, R and S respectively. Move one of the vertices of the quadrilateral ABCD. What do you notice about the quadrilateral PQRS? Make a conjecture about PQRS and prove your conjecture.

To move a vertex, click and drag on the green handles.