PLANK TKHiOXOMICTRY. 79 



listances of any point P on a circle from the an- 

 gular points of a regular polygon of n sides inscribed in the circle 

 uiv the positive roots of th.- relation 



d being the diameter of the circle and 6 the angle subtended at 

 1 y any one of the distances. 



377. The sides of a convex quadrilateral are a, b, c y d and 

 2* is their sum ; prove that 



j8(8-a-d)(8-b-d)(8-c-d) 

 t be greater than the area of the quadrilateral. 



378. The equation giving the length x of the diagonal joining 

 the angles (a, d), (b, c) of a quadrilateral, whose sides taken in 



: are a, b, c, d, is 



{x 9 (ab + cd) -(ac + bd) (ad + be)} 9 



= tabcd cos' a {(x 9 -a t -b<)(x 9 -c 9 - d') + tabcd sin 8 a}; 

 ing the sum of two opposite angles. 



.. In any <iua.liilat.ral ABCD, BC y AD nu -. -t in 

 and AB y CD'mG', prove that 



(EB.EC-EA.ED)* (PC . FA - FB . FD) 9 



EA . J'JJ . EC.KU a iu' E FA . t'JJ . 'M"FJ> sin" /' 



l.GC. OD sin'C? * 



