Given trapezoid ABCD with parallel sides AB and CD, let E be a point on line BC outside segment BC, such that segment AE intersects segment CD. Assume that there exists a point F inside segment AD such that ∠EAD=∠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, and assume that K is different from I and J.Prove that K belongs to the circumcircle of △ABI if and only if K belongs to the circumcircle of △CDJ. geometrytrapezoidcircumcirclegeometry proposed