Problem

Source: 2013 JBMO Shortlist G2

Tags: geometry, JBMO



Circles ω1 , ω2 are externally tangent at point M and tangent internally with circle ω3 at points K and L respectively. Let A and B be the points that their common tangent at point M of circles ω1 and ω2 intersect with circle ω3. Prove that if KAB=LAB then the segment AB is diameter of circle ω3. Theoklitos Paragyiou (Cyprus)