Calendar: 1888-1889 Page 745

ENGINEERING DEPARTMENT 737 II UKatljrmattai UfucliU ant Crignnomctrn Prove that the opposite angles of quadrilateral in scribed in circle are equal to two right angles Prove that the bisectors of the angles of triangle meet in point Also prove that the bisectors of the internal and external angles meet three by three in four points which are such that the join of any two is at right angles to the join of the other Give construction for the circnmcentre of triangle In what case is the circumcentre outside the triangle is any point in the base AB of an isosceles triangle ABC prove that the circumcircles of ADC BBC are equal Define similar figures Prove that triangles that are equiangular to one another are similar On the sides AB AC of triangle are taken points Ε such that ABC AED are similar triangles prove that BCEB are concyclic On each side of right-angled triangle regular pen tagon is described prove that the pentagon described on the hypothenuse is equal to the sum of the pentagons described on the sides What is meant by the angle between two planes What by the angle between two straight lines that do not intersect Three tangent lines to sphere are mutually at right angles and do not intersect what is the angle between the lines joining the points of contact Define the tangent of an angle The tangent of an angle is £ txpress the sine and the secant Prove that cos ii cos cos Β si11 sin sin sin Β ο sin--- c08 Β