Calendar: 1886-1887 Page 735

CLOTHWORKERS SCIENCE EXHIBITIONS 737 base shall have the same ratio which the other sides of the triangle have to one another and if the segments of the base have the same ratio which the other sides of the triangle have to one another the straight line drawn from the vertex to the point of section shall bisect the vertical angle The straight lines which bisect the angles of triangle meet at the same point 10 The rectangle contained by the diagonals of quad- rilateral figure inscribed in circle is equal to both the rectangles contained by its opposite sides 11 Find the equation to straight line in terms of the intercepts on the axes Given point and two fixed lines draw any two lines through the fixed point and join transversely the points where they meet the fixed lines find the locus of the inter- section of the transverse lines 12 Find the form of the equation to straight line which is at right angles to given straight line Show that the diagonals of the parallelogram formed by the straight lines £ £ £ £ £ are at right angles 13 Find the equation to the circle referred to any axes and deduce its equation when referred to pair of tangents inclined at an angle of 60 as axes 14 If the normal at the point Ρ of parabola meet the axis in the point then NG 2AS If be the middle point of SG and the foot of the directrix then QX2 QP2 4AS2 15 If be an ordinate to the diameter PV of parabola then QV2 4SP PP If QD be drawn at right angles to the diameter PV then QD2 4AS PV 16 Al are the vertices of an ellipse Ρ any point on the curve show that if Ρ Ν be perpendicular to AP and PM perpendicular to A'P Μ and Ν being on the axis AA' then will MN be equal to the latus rectum of the ellipse