Calendar: 1877-1878 Page 560

558 FREAKE EXHIBITIONS Produce given straight line so that the rectangle contained by the line produced and the part produced may he equal to given square Describe square equal to given rectangle The opposiie angles of quadrilateral figure inscribed in circle are equal to two right angles If quadrilateral be described about circle the angles subtended at the centre of the circle by any two opposite sides the figure are together equal to two right angles Describe an isosceles triangle with each angle at the base double the vertical angle 10 In the last question shew that the base of the triangle is equal to the side of regular pentagon inscribed in the smaller circle of the figure 11 Similar triangles are to one another in the duplicate ratio of tlieir homologous sides 12 Describe rectilineal figure similar to one and equal to another rectilineal figure 13 ABCDEF is regular hexagon Shew that BF divides AD in the ratio of to 14 In the parabola prove that QF' SP PF where QV an ordinate to any diameter PF 15 Draw pair of tangents to parabola from an external point If OQ OQ' be tangents and OV parallel to the axis meet the directrix in and QQ1 meet the axis in then OKNS is parallelogram 16 In an ellipse if CD be conjugate to CP then CP will be conjugate to CD 17 Find the area of triangle in terms of the cooidinates of ts angular points 18 Find the equation to circle referred to pair of tangents as axes when they are at right angles when inclined at an angle ω 19 Find the equation to the tangent to parabola at given point to the pair of tangents drawn from given point to the chord joining the points of contacted the pair of tangents