IMO 2009 Shortlist G6
Let the sides AD and BC of the quadrilateral ABCD (such that AB is not parallel to CD) intersect at point P. Points O1 a...
Category: Geometry
Problem
Let the sides AD and BC of the quadrilateral ABCD (such that AB is not parallel to CD) intersect at point P. Points O1 and O2 are the circumcenters and points H1 and H2 are the orthocenters of triangles ABP and DCP, respectively. Denote the midpoints of segments O1H1 and O2H2 by E1 and E2, respectively. Prove that the perpendicular from E1 on CD, the perpendicular from E2 on AB and the line H1H2 are concurrent.