The quadrilateral ABCD is inscribed in the circle ω with the center O. Suppose that the angles B and C are obtuse and lines AD and BC are not parallel. Lines AB and CD intersect at point E. Let P and R be the feet of the perpendiculars from the point E on the lines BC and AD respectively. Q is the intersection point of EP and AD,S is the intersection point of ER and BC. Let K be the midpoint of the segment QS . Prove that the points E,K, and O are collinear. geometrycollinearcyclic quadrilateralperpendicular