# Calendar: 1899-1900 Page 763

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FACULTY OF SCIENCE CXI Λ יי ί λλ tiTA Λ if' Γ יי tremities intersect the fixed chord in points equidistant from the centre Circumscribe circle about given triangle If the three perpendiculars of an acute angled triangle are produced to meet the circumference of the circum-circle and each of the three points is joined to the two nearest angular points of the triangle prove that the hexagon so formed is twice the area of the triangle What is the rule for calculating the length of circular arc whose chord and the chord of its half are given Use this rule indirectly for finding the perimeter ap- proximately of regular octagon inscribed in circle of radius 10 inches and shew that the error made is less than tenth of an inch rectangular piece of paper ABCD has its breadth BC equal to inches It is folded over once so that lies on AB at distance inches from It is then un- folded and torn in two along the crease Prove that the area of the triangle so cut off is α2 δ2 8αδ What is Orthogonal Projection By means of geometrical construction in plane deter mine the orthogonal projection on plane of given angle ABG lying in another plane Β and BC being both inclined to the line of intersection of the planes Ρ and Define Harmonic Section Λ יי י Prove geometrically that the Geometric Mean of two finite straight lines is also the Geometric Mean of the Arithmetic and Harmonic Means of the same lines The inscribed circle of right angled triangle ABC touches the hypotenuse AB at and is the foot of the perpendicular from on AB Prove that CD is harmonic mean between AX and BX Two spheres have radii and and the line joining their nearest points is Find point on this line from which equal surfaces of each sphere are visible 10 milk can is in the shape of frustum of right circular cone The circumferences of the top and bottom are respectively 34 inches and 56 inches and the slant height is 22 inches Find the number of gallons it contains given tl at gallon is equivalent to 277274 cubic inches

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