Tangential quadrilateral all of whose sides are tangent to a single conic section has three diagonals that meet at a point. From a tangential quadrilateral, one can form a hexagon with two 180° angles, by placing two new vertices at two opposite points of tangency; all six of the sides of this hexagon lie on lines tangent to the inscribed circle, so its diagonals meet at a point. But two of these diagonals are the same as the diagonals of the tangential quadrilateral, and the third diagonal of the hexagon is the line through two opposite points of tangency. Repeating this same
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