Calendar: 1882-1883 Page 632

general literature and science 629 If two triangles having their vertical angles equal stand on the same base and on the same side of it they have the same circumscribing circle To describe circle about given triangle If the inscribed and circumscribed circles be concentric the triangle is equilateral The sides about the equal angles of triangles which are equiangular to one another are proportionals and those which are opposite to the equal angles are homologous sides If from any point in the circumference of circle perpen- diculars- are drawn to two tangents and to their chord of contact the rectangle under the first two perpendiculars is equal to the square on the latter Express the area of triangle in terms of the rectangular the polar co-ordinates of its angular points Draw the lines -f- χ χ 1ל and find the area they contain Find the equations to the straight lines which pass through given point and make given angle with given straight line Find the equations to the straight fines which pass through the origin and are inclined at an angle of 75 to the straight line -f χ V3 What is the necessary condition that three straight lines meet in point Show that the lines drawn from the angles of triangle to the bisections of the opposite sides meet in point 10 Show that an equation of the form Ax By Ε in general represents circle and note the exceptional cases Find the equation to the circle circumscribing an equi- lateral triangle taking an angular point as origin Deduce the polar equation 11 If the tangent at any point Ρ of parabola meet the axis produced in the point and the tangent at the vertex in then SY will bisect Ρ Τ at right angles