Calendar: 1876-1877 Page 553

CLOTHW OEKERS SCIENCE EXHIBITION 553 fan2 cos β ens χ cos tan2 β cos α ουκ χ cos then tan2- tan tan2 11 Eliminate θ from the equations cosec sin θ sec θ cos 12 Solve triangle when two sides are given and the included angle 13 Find the radii of the inscribed circumscribed and escribed circles of triangle 14 Define the nine point circle and prove its chief properties II romttrt Draw straight line perpendicular to given straight line of an unlimited length from given point without it All the interior angles of any rectilineal figure together with four right angles are equal to twice as many right angles as the figure has sides The opposite angles of parallelogram are equal to one another and the diameter bisects the parallelogram Prove also that the diameters bisect each other In any triangle the square on the side subtending an acute angle is less than the squares on the sides containing that angle by twice the rectangle contained by either of these sides and the straight line intercepted between the perpendicular let fall on it from the opposite angle and the acute angle Describe square equal to given rectangle β The opposite angles of any quadrilateral figure inscribed in circle are equal to two right angles Prove also the converse Draw pair of tangents to circle from an external point Describe an isosceles triangle having each of the angles of the base double the third angle