Calendar: 1893-1894 Page 836

cxiv FACULTY OF SCIENCE III -i$latf emattc JPttditi -IV YEAR Shew how to draw straight line perpendicular to given straight line of unlimited length from given point without it Prove without using any subsequent propositions that only one such perpendicular could be drawn Prove that the three interior angles of any triangle are together equal to two right angles On AB AC sides of triangle ABC right-angled at equilateral triangles ADB AEC are described on the sides remote from and Β CD and BE are joined shew that the sum of the angles CDB BEC is right angle If straight line be bisected and produced to any point the rectangle contained by the whole line produced and the part of it produced together with the square on half the line bisected is equal to the square on the line made up of the half and the part produced Shew how to divide given straight line so that the rect- angle contained by the whole line and one part may be equal to twice the square on the other part In equal circles equal angles stand on equal arcs whether they be at the centres or at the circumferences ABC is triangle inscribed in circle CD is drawn per- pendicular to BC to meet the circle in and DE perpen- dicular to CD to meet the circle in Ε shew that if CA CB then Ε is the mid-point of the arc AB Shew how to describe on given straight line segment of circle containing an angle equal to given rectilineal angle iX If ABC be triangle and with the incentre as centre another circle is described cutting the sides BC CA AB in the points Ε Η Κ in order prove that DE FG HK and that the triangle KGE is equal to the triangle HFD in all respects