BOOK OF MATHEMATICAL PROBLEMS. 



GEOMETRY. 



1. A POINT is taken within a polygon ABC...KL : prove 

 that OA, OB...OL are together greater than half the perimeter of 

 the polygon. 



2. Two triangles are on the same base and between the same 

 parallels; through tin- point of intersection of their sides is drawn 

 a straight line parallel to the base and terminated by the si.l - 

 which do not intersect: prove that the segments of this straight 

 line are equal. 



The sides Afi, AC of a triangle ore bisected in /'. /.', and 

 ' 'I i, Hi: intersect ii ve that the triangle BFC is equal to 



quadrilateral ADFJ- 



4. AS, CD ore two parallel straight line*, the mid.ll. 

 of CD, and /', G the respective points of intersection of 

 AC, BE and of A t BD : prove that FG is parallel to J /;. 



6. In any quadrilateral the squares on the sides together 

 exceed the squares on the diagonals by the square on twice the 

 < 4 the middle points of the diagonals. 



G. If a straight line be divided in extreme and mean i 

 reduced so that the part produced is equal to the smaller of 

 gmente, the rectangle contained by the whole line tit us pro- 



I 



