Calendar: 1884-1885 Page 636

630 GENERAL LITERATURE AND SCIENCE ABCD is parallelogram and Fy the middle points of AD and BC respectively Show that BE and OF will bisect the diagonal If straight line be divided into two equal parts and also into two unequal parts the rectangle contained by the unequal parts together with the square on the line between the points of section is equal to the square on half the line If from the right angle of right-angled triangle per- pendicular be drawn to the hypotenuse it divides the hypo- tenuse into segments the rectangle under which is equal to the square of the perpendicular Equal straight lines in circle are equally distant from the centre and those which are equally distant from the centre are equal to one another From given point to draw straight line cutting given circle so that the intercepted chord shall be of given length The angles in the same segment of circle are equal and Β are two given points on the same side of given straight line and Β produced meets this line at of all points in the given straight line on each side of to deter- mine that at which Β subtends the greatest angle If from any point without circle two straight lines are drawn one of which cuts the circle and the other touches it the rectangle contained by the whole line which cuts the circle and the part of it without the circle is equal to the square on the line which touches it If ADy CE are drawn perpendicular to the sides BC AB of triangle ABC show that the rectangle contained by BC and BD is equal to the rectangle contained by Β and BE To describe circle about given triangle If the inscribed and circumscribed circles of triangle are concentric the triangle is equilateral To describe an isosceles triangle having each of the angles at the base double of the third angle I£ the vertical angle of triangle oe bisected by straight line which also cuts the base the segments of the