Problems(1)
Let ABC be a triangle with AC>BC, let ω be the circumcircle of △ABC, and let r be its radius. Point P is chosen on AC such taht BC=CP, and point S is the foot of the perpendicular from P to AB. Ray BP mets ω again at D. Point Q is chosen on line SP such that PQ=r and S,P,Q lie on a line in that order. Finally, let E be a point satisfying AE⊥CQ and BE⊥DQ. Prove that E lies on ω.
geometry