# Calendar: 1896-1897 Page 690

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c FACULTY OF SCIENCE dFacttlti of Sctenire -Β limit tin FIUST YEAE The same paper as set for the Faculty of Arts Π -jWati cn1attr$ Guditt -IV an $lane flfliensHiratioii YEAR Any two sides of triangle are together greater than the third Prove that the perimeter of convex hexagon is greater than the sum of any two of the three straight lines joining opposite angular points of the hexagon If straight line be divided into any two parts the square on the whole line is equal to the sum of the squares on the parts together with twice the rectangle contained by them If straight line ABis divided at prove that the square whose diagonal is AB exceeds the sum of the squares whose diagonals are AC CB by the rectangle AC CB Angles in the same segment of circle are equal If through the two points of intersection of two circles pair of straight lines be drawn and produced both ways to meet the circles prove that the straight lines joining their extremities will be parallel Hence or otherwise show that if two circles touch at and straight line PAQ be drawn through to cut the circles at Ρ and the tangents at Ρ and will be parallel If from any point without circle tangent and

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