Calendar: 1891-1892 Page 815

engineering department cxxv11 one side of the one equal to the hypothenuse and one side of the other they shall be equal in all respects 15 If straight line be divided into any two parts the squares on the whole line and on one part shall be equal to twice the rectangle contained by the whole and that part together with the square on the other part 16 From any point within circle that is not the centre two and only two equal straight lines can be drawn to the circumference 17 If two circles cut prove that the common chord is at right angles to the line joining their centres Hence prove that if two circles touch the line joining their centres passes through the point of contact 18 segment of circle being given describe tl of which it is segment How can you tell whether the segment is greater equal to or less than semi-circle 19 Through the mid-point of the radius OA of circle Β Ε AC CDE is drawn perpendicular to the diameter BOA EO produced meets the circumference in prove that BC is perpendicular to EF 20 Inscribe regular hexagon in given circle and thence shew how to describe regular hexagon about given circle From these figures shew that the ratio of the length of the circumference of circle to the diameter is between and 3J FIRST SECOND AND THIRD YEARS Crtgonometrn Shew how the distance between two inaccessible points may be obtained are four points in the same plane if the angles PAQ PBQ are equal then PQ AB sin PAQ sin APB Prove that in any triangle tan where the usual meanings are attached to the letters If the triangle is equilateral the radii of the inscribed circumscribed and escribed circles are in the ratios