CZ-SK-MO 2006 Problem 3

In a scalene triangle $ABC$ ,the bisectors of angle $A,B$ intersect their corresponding sides at $K,L$ respectively. $I,O,H$ denote respectively the incenter,circumcenter and orthocenter of triangle $ABC$ . Prove that $A,B,K,L,O$ are concyclic iff $KL$ is the common tangent line of the circumcircles of the three triangles $ALI,BHI$ and $BKI$ .