The line ℓ is perpendicular to the side AC of the acute triangle ABC and intersects this side at point K, and the circumcribed circle △ABC at points P and T (point P on the other side of line AC, as the vertex B). Denote by P1 and T1 - the projections of the points P and T on line AB, with the vertices A,B belong to the segment P1T1. Prove that the center of the circumscribed circle of the △P1KT1 lies on a line containing the midline △ABC, which is parallel to the side AC. (Anton Trygub) geometryCircumcentermidline