Calendar: 1875-1876 Page 543

FREAKE EXHIBITIONS 539 Show that the base of the triangle is equal to the side of regular pentagon inscribed in the smaller circle The rectangle contained by the diagonals of quadrilateral inscribed in circle is equal to both the rectangles contained by its opposite sides Draw the lines χ 2y δ 2x χ and find the area of the triangle they include 10 The straight lines drawn through the middle points of the sides of triangle respectively perpendicular to those sides meet at point 11 If the line be tangent to the circle x2 y2 cl find the relation between and 12 Show how to draw pair of tangents to parabola from an external point Prove that the tangents so drawn subtend equal angles at the focus the circle which passes through the intersections of three tangents to parabola will pass through the focus 13 In triangle ABC if tan tan and Β be fixed Δ the locus of is parabola with vertex and focus 14 In the ellipse the perpendiculars from the foci on the tan- gent intersect the tangent in the circumference of circle having the axis major as diameter 15 In the ellipse the sum of the squares of two conjugate semi-diameters is constant If through the foci and Η chords PSP' and QHq be drawn parallel to any pair of conjugate diameters show that SP SP HQ Hq 62 16 Find the equation to the hyperbola the asymptotes being axes and deduce from it the equation to the tangent -eEttglurt tsitorj Give some account of the condition of the Britons Ca3s ir's landing