Let ABCD be a convex cyclic quadrilateral satisfying AB⋅CD=AD⋅BC. Let the inscribed circle ω of triangle ABC be tangent to sides BC, CA and AB at points A′,B′ and C′, respectively. Let point K be the intersection of line ID and the nine-point circle of triangle A′B′C′ that is inside line segment ID. Let S denote the centroid of triangle A′B′C′. Prove that lines SK and BB′ intersect each other on circle ω.Proposed by Áron Bán-Szabó, Budapest geometryHarmonic Quadrilateralprojective geometrykomal