Online Geometry Problem 911: Right Triangle, Double Angle, Triple Angle, Concyclic Points, Cyclic Quadrilateral. Level: High School, College, Mathematics Education

The figure shows a right triangle ABC, D is on AC extended and E on AB extended, angle A = 2(angle CBD), and angle BCE = 3(angle CBD). Prove that the points B, C, D, and E are concyclic ((lie on a same circle).