In an acute triangle ABC the angle ∠C is greater than ∠A. Let E be such that AE is a diameter of the circumscribed circle Γ of \vartriangle ABC. Let K be the intersection of AC and the tangent line at B to Γ. Let L be the orthogonal projection of K on AE and let D be the intersection of KL and AB. Prove that CE is the bisector of ∠BCD. geometrycircumcircleangle bisector