Problem

Source: Middle European Mathematical Olympiad 2011 - Individuals I-3

Tags: geometry, circumcircle, geometric transformation, reflection



In a plane the circles K1 and K2 with centers I1 and I2, respectively, intersect in two points A and B. Assume that I1AI2 is obtuse. The tangent to K1 in A intersects K2 again in C and the tangent to K2 in A intersects K1 again in D. Let K3 be the circumcircle of the triangle BCD. Let E be the midpoint of that arc CD of K3 that contains B. The lines AC and AD intersect K3 again in K and L, respectively. Prove that the line AE is perpendicular to KL.