Problem

Source: 2009 Cuba 2.6

Tags: geometry, collinear



Let ω1 and ω2 be circles that intersect at points A and B and let O1 and O2 be their respective centers. We take M in ω1 and N in ω2 on the same side as B with respect to segment O1O2, such that MO1BO2 and BO1NO2. Draw the tangents to ω1 and ω2 through M and N respectively, which intersect at K. Show that A, B and K are collinear.