Calendar: 1851-1852 Page 317

GENERAL LITERATURE AND SCIENCE JUNIOR MATHEMATICAL SCHOLARSHIP The square described upon the hypothenuse of right- angled triangle is equal to the sum of the squares on the sides which contain the right angle Show that Β Κ and pass through the same point Divide straight line into two parts so that the rectangle of the whole and one of the parts shall be equal to the square of the other part Find the point 77 algebraically Is the question numerically possible The opposite angles of any quadrilateral inscribed in circle are together equal to two right angles The squares of the sides of quadrilateral figure are greater than the squares of its diagonals by times the square of the line joining the middle points of the diagonals Inscribe circle in given triangle Find the radius of the inscribed circle and if two sides of the triangle be produced describe circle which shall touch the two sides produced and the third side and if r2 r3 be the radii of the three circles escribed show that- Area of triangle r2 r3 If two triangles have one angle of the one equal to one angle of the other and the sides about the equal angles propor- tionals the triangles shall be equiangular If two straight lines be parallel and one of them be at right angles to plane the other shall be at right angles to the same plane Find the sum of all the lines that can be drawn from one of the angles of regular polygon to the remaining angles 10 The radius of the earth 000 miles subtends at the centre of the sun an angle of 8" 57 find the sun's distance from the earth