In an acute triangle ABC the angle C is greater than the angle A. Let AE be a diameter of the circumcircle of the triangle. Let the intersection point of the ray AC and the tangent of the circumcircle through the vertex B be K. The perpendicular to AE through K intersects the circumcircle of the triangle BCK for the second time at point D. Prove that CE bisects the angle BCD. geometrycircumcircleangle bisectorperpendiculartangent