A circle is divided by the chord AB into two segments and one of them is rotated about the point A by a certain angle, the point B being taken to B′. Prove that the line segments joining the midpoints of the two arcs (i.e. the arc AB which had not been rotated and the rotated arc AB′) with the midpoint of BB′ are perpendicular.(F. Nazyrov, 11th form student, Obninsk) rotationgeometryperpendicular