IMO 2011 Shortlist G3
Let ABCD be a convex quadrilateral whose sides AD and BC are not parallel. Suppose that the circles with diameters AB an...
Category: Geometry
Problem
Let ABCD be a convex quadrilateral whose sides AD and BC are not parallel. Suppose that the circles with diameters AB and CD meet at points E and F inside the quadrilateral. Let ωE be the circle through the feet of the perpendiculars from E to the lines AB, BC, and CD. Let ωF be the circle through the feet of the perpendiculars from F to the lines CD, DA, and AB. Prove that the midpoint of the segment EF lies on the line through the two intersection points of ωE and ωF .