58 EXAMPLES 



But.l AT and BK are |uuli 



two ci ust coincide: that is, the poiij- //. t' lie 



on tin- cireumierencc of a 



this way we shew that any f<ur ronsm 

 points of the polygon lie on the circumference of a < 

 and hence it follows that all t: Lax points m 



the circr of the same circle. 



..ill be seen from the prm-din;.: results that 1: 



is the id is denoted by the product of 



fi into the radius of the circle described round the polygon. 



EXAMPLES. 



1. ABCD is a quadrilateral and is aeted on by f< 

 which are represented in magnitude and direction by .11!. 

 AD, CB, CD-, shew that the resultant coincides in 



with the straight line which joins the middle points of the 

 diagonals A C, BD, and is represented in magnitude by four 

 times this straight line. 



2. Forces whose intensities are proportional to : 

 of an isosceles triangle act along tne sides of the tri, 

 those acting along the equal sides tending from the vertex; 

 find the magnitude and position of their resultant. 



Ilesult. The required resultant is represented by a straight 

 line which passes through the middle point of the base of the 

 _de, is parallel to one of the sides, and double that side 

 in length. 



3. The upper end of a uniform heavy rod rests a:: 



a smooth vertical wall; one end of a string is 1 to the 



lower end of the rod and the other end of the string is fa.- 

 to the wall; the position of the rod ' . ii i id tin -point 



of the wall to which the string mu.- ned. in oid r that 



the rod may be in equilibrium. 



4. rm heavy rod is placed across a smooth hori- 

 zontal rail, and rests with one end against a smooth vertical 



