We assign to any quadrilateral ABCD the centers of the circles circumscribed in the triangles BCD, CDA, DAB, ABC. Prove that if the vertices of a convex quadrilateral Q do not lie on the circle, thena) the four points assigned to quadrilateral Q in the above manner are the vertices of the convex quadrilateral. Let us denote this quadrilateral by t(Q),b) the vertices of the quadrilateral t(Q) do not lie on the circle,c) quadrilaterals Q and t(t(Q) are similar. geometrysimilaritysimilar