Let $$Ω_{1}, Ω_{2}$$ be two intersecting circles with centres $$O_{1},O_{2}$$ respectively, Let $$l$$ be a line that intersects $$Ω_{1}$$ at points $$A, C$$ and $$Ω_{2}$$ at points $$B, D$$ such that $$A, B, C, D$$ are collinear in that order. Let the perpendicular bisector of segment AB intersect $$Ω_{1}$$ at points $$P, Q$$; and the perpendicular bisector of segment CD intersect $$Ω_{2}$$ at points $$R, S$$ such that $$P, R$$ are on the same side of l. Prove that the midpoints of P R, QS and $$O_{1},O_{2}$$ are collinear.