IMO 2014 Shortlist G7
Let ABC be a triangle with circumcircle Ω and incentre I. Let the line passing through I and perpendicular to CI interse...
Category: Geometry
Problem
Let ABC be a triangle with circumcircle Ω and incentre I. Let the line passing through I and perpendicular to CI intersect the segment BC and the arc BC (not containing A) of Ω at points U and V , respectively. Let the line passing through U and parallel to AI intersect AV at X, and let the line passing through V and parallel to AI intersect AB at Y . Let W and Z be the midpoints of AX and BC, respectively. Prove that if the points I, X, and Y are collinear, then the points I, W, and Z are also collinear. (U.S.A.) Shortlisted problems 9