Hexagon circle) with vertices given by the six intersections of the edges of a triangle and the three lines that are parallel to the edges that pass through its symmedian point. If the successive sides of a cyclic hexagon are "a", "b", "c", "d", "e", "f", then the three main diagonals intersect in a single point if and only if . If, for each side of a cyclic hexagon, the adjacent sides are extended to their intersection, forming a triangle exterior to the given side, then the segments connecting the circumcenters of opposite triangles are concurrent. If a hexagon has vertices
Boy with a Glass and a Lute hand a glass full of wine, at which he looks with a smile. His dark costume is trimmed with blue ; his cap hangs on the back of his head, to the left. With his left hand he holds up one end of a mandoline, the other end of which rests on a table. Signed on the right with the monogram ; panel, 36 inches by 30 inches. Exhibited at the Royal Academy Winter Exhibition, London, 1891, No. 72." Hals' positioning of a figure looking upwards was common to many of his genre paintings of the 1620s: This painting is