Calendar: 1871-1872 Page 577

the school 577 Divide straight line into two parts so that the rectangle contained by the whole and one of tbe parts shall be equal to the square of the other part Prove that the squares on the whole and the former part are equal to three times the square on the other part Enunciate the Twelfth Proposition of the Second Book with respect to obtuse-angled triangles Triangles are described upon the same base and having the difference of tbe squares of the other sides constant show that the vertex of any triangle is on one or other of two fixed straight lines Draw pair of tangents to circle from an external point The tangents from point Ο are bisected by straight line which meets chord PQ of the circle in prove that the angles ROP OQR are equal The opposite angles of any quadrilateral figure inscribed in circle are together equal to two right angles Find triangle such that the feet of the perpendiculars from the angular points on tbe opposite sides shall coincide with tbe angular points of given triangle Inscribe circle in given triangle Through fixed point on tbe bisector of given angle line is drawn to meet the sides containing the angle determine when the radius of the circle inscribed in the triangle is maximum The sides about the equal angles of equiangular triangles are proportional Inscribe parallelogram in given triangle so that its diago- nals may intersect at given point within the triangle 10 Describe rectilineal figure similar to one and equal to another rectilineal figure 11 In right-angled triangle any rectilineal figure described upon the side opposite to the right angle is equal to the similar and similar-described figures upon the sides containing the right angle 12 Draw straight line perpendicular to plane from given point above it ο