Calendar: 1899-1900 Page 756

civ FACULTY OF SCIENCE If three circles intersect one another prove that their common chords are concurrent Prove that the lines joining the centres of the escribed circles of triangle pass through its angular points If 11ך I2 I3 are the excentres and the incentre of the triangle ABC shew that IXA 12A IZA How many spherical balls each of 10 inches radius can be contained in hollow closed cylinder internal diameter 30 inches and height yards If the cylinder be placed upright what will be the dis tance between the uppermost ball and the top of the cylinder cube and regular octahedron have equal volumes find the ratio of their surfaces Two cylindrical buckets each of internal diameter ft and depth ft hang round wheel by chain weighing lbs per foot over well 350 ft deep so that when one end of the chain is just touching the water the other end is just on the wheel If the full bucket be hauled up how far will it ascend before the weight of the empty bucket and des- cending chain will counterbalance the weight of the full one and ascending chain cubic foot of water weighs 1000 ounces 10 Trace for the same axes tt -ώ from to and find approximately the points of intersection of the two curves l-zm λ' "י 11 line is drawn through the middle point of the base BC of triangle meeting the sides AB AC in Ρ and and line through parallel to BC in Prove that the range PXQ is harmonic 12 Demonstrate the method of finding the radius of gyration of body about an axis when the radius of gyration about another parallel axis is known Find the radius of gyration of uniform circular disc about an axis perpendicular to its plane passing through point in its circumference