Calendar: 1886-1887 Page 680

682 GENERAL LITERATURE AND SCIENCE If the side BO of triangle ABO be bisected at and the angles ABB ADO be bisected by the straight lines DE and DF meeting AB AC in respectively show that EF um parallel to BC In right-angled triangle if perpendicular be drawr from the right angle to the base the triangles on each side 0J it are similar to the whole triangle and to one another If the triangle ABO has the angle at right angle anc from perpendicular be dropped on the opposite side inter- secting it in prove that AD DB AO2 BO2 If two straight lines be parallel and one of them be a1 right angles to plane prove that the other is also at right angles to the same plane Also prove that if one of these straight lines be inclined a1 any angle to particular plane the others will be inclined at the same angle to the same plane Define solid angle and prove that if solid angle be contained by three plane angles any two of them are togethei greater than the third In parabola show that the abscissa of any point on the curve varies as the square of the semiordinate to the axis If parabola roll on an equal parabola the vertices originally coinciding prove that the focus of the rolling one traces out the directrix of the fixed parabola Having given the foci show how to describe an ellipse which touches given straight line Find the coordinates of the point of intersection of the two lines 2x and 4x 3y and also find the distance of this point from the line 2y χ Prove that the equation 3y2 8xy Sx2 9y 7x represents two straight lines which are at right angles to each other 10 The equation to circle referred to rectangular co ordinates being 2x2 ty2 806 12 ל find its radius and the position of its centre 11 if c9 be the lengths of two choids of circle which