Calendar: 1898-1899 Page 743

FACULTY OF SCIENCE cxi escribe triangle having given the base the difference of the sides and the difference of the base angles Shew that if twice the greater of the base angles exceeds the less by right angle there will be only one solution If straight line be divided equally and unequally prove that the sum of the squares on the unequal parts is double of the sum of the squares on half the line and on the line between the points of section Hence prove that if the vertex of triangle ABC be joined to Ο the mid-point of BC Β A2 AC2 A2 OB2 The straight line joining the centres of two intersecting circles bisects their common chord at right angles Deduce that the line joining the centres of two circles that touch internally or externally passes through their point of contact The angle in semicircle is right angle the angle in segment less than semicircle is greater than right angle and the angle in segment greater than semicircle is less than right angle If is fixed point on circle PQ any diameter and the line joining to the mid-point of Ρ is produced to so that QH RS prove that the loci of and א are circles On the sides of triangle outwards equilateral triangles are described and circles are described round these triangles prove that these circles meet in point Ascertain whether the point of meeting is within or without the triangle Find the perimeter and area of regular octagon de- scribed about circle of ft radius State IIuygen'8 rule for finding approximately the length of circular arc Find approximately the area of segment of circle whose chord is 121 ft and height 11 ft Also find the radius of the circle CJ Inscribe circle in given triangle Through the angular points of triangle ABC are drawn lines perpendicular to the bisect org of the angles of the tri- angle forming triangle AlBiC from this triangle another 14