IMO Shortlist 2005 problem G1

  Avg: 3,3
  Avg: 6,0
Given a triangle ABC satisfying AC+BC=3\cdot AB. The incircle of triangle ABC has center I and touches the sides BC and CA at the points D and E, respectively. Let K and L be the reflections of the points D and E with respect to I. Prove that the points A, B, K, L lie on one circle.
Izvor: Međunarodna matematička olimpijada, shortlist 2005