Calendar: 1866-1867 Page 470

472 GENERAL LITERATURE AND SCIENCE 14 Through given point within an angle PAQ to draw line PBQ which shall include with AP and AQ the greatest triangle 15 The base and the vertical angle of triangle being given determine the triangle such that the sum of the radii of the circles inscribed in the triangle and escribed on the base may be minimum FIRST YEAR -Slant Crigononutrj hexagon is inscribed in circle radius and the alternate angles are joined the joining lines forming another hexagon Prove that the area of this last hexagon £ γ Find when sec sec cos If tan find the value of the fraction sin2 cos sin2 cos 2A are three angles in the proportion of and 7r their sum is show that their tangents are in arithmetical progression If be the angle of triangle of which the sides are prove that cos £ tan Cf If χ prove that aV