Let ABCD be a parallelogram. Half-circles ω1,ω2,ω3 and ω4 with diameters AB,BC,CD and DA, respectively, are erected on the exterior of ABCD. Line l1 is parallel to BC and cuts ω1 at X, segment AB at P, segment CD at R and ω3 at Z. Line l2 is parallel to AB and cuts ω2 at Y, segment BC at Q, segment DA at S and ω4 at W. If XP⋅RZ=YQ⋅SW, prove that PQRS is cyclic.Proposed by José Alejandro Reyes González Mexicogeometryparallelogrampower of a point