IMO 2008 Shortlist G2
Given trapezoid ABCD with parallel sides AB and CD, assume that there exist points E on line BC outside segment BC, and ...
Category: Geometry
Problem
Given trapezoid ABCD with parallel sides AB and CD, assume that there exist points E on line BC outside segment BC, and F inside segment AD, such that ∠DAE = ∠CBF. Denote by I the point of intersection of CD and EF, and by J the point of intersection of AB and EF. Let K be the midpoint of segment EF; assume it does not lie on line AB. Prove that I belongs to the circumcircle of ABK if and only if K belongs to the circumcircle of CDJ.