Calendar: 1873-1874 Page 548

548 GENERAL LITERATURE AND SCIENCE If two circles intersect the common chord produced bisects the common tangent 10 To inscribe an equilateral and equi-angular pentagon in given circle 11 The sides about the equal angles of triangles which are equi-angular to one another are proportionals and those sides which are opposite to the equal angles are homologous that is are the antecedents or the consequents of the ratios 12 If perpendiculars be drawn from any point on the circum- ference of circle to two tangents and their chord of contact the square on the perpendicular to the chord is equal to the rectangle under the other two perpendiculars 13 Similar triangles are to one another in the duplicate ratio of their homologous sides 14 The rectangle contained by the diagonals of quadrilateral figure inscribed in circle is equal to both the rectangles con- tained by its opposite sides 15 To draw common tangent to two circles 16 If two exterior angles of tiiangle are bisected and from the point of intersection of the bisecting lines line be drawn to the opposite angle of the triangle it will bisect that angle 17 Find by geometrical construction an Arithmetic Geo- metric and Harmonic mean between two given straight lines VII -analutiral comrtvi Find the length of the perpendicular from the vertex of triangle upon the base the co-ordinates of the vertex being and those of the extremities of the base and Express the area of triangle in terms of the co-ordinates of its angular points and find the area included between the lines χ tan χ tan a2 χ tan a3 -f Find the equation to the line which is equidistant from the two lines represented by the equations mx