STATICS. 



I. Composition and Resolution of Forces. 



1211. If be the centre of the circle circumscribing a tri- 

 angle ABC, and D, E, F the middle points of the sides, the 

 system of forces OA, OB, OC will bo equivalent to the system 

 OD, OE, OF. 



1-212. Forces P, Q, R act along the sides of a triangle ABC 

 and their resultant passes through the centres of the inscribed 

 and circumscribed circles ; prove that 



P Q R 



cos B - cos G~ cos C - cos A ~~ cos A- COB ' 



1213. ABCD is a quadrilateral inscribed in a circle, and 

 forces inversely proportional to AB, BC, AD, DC act along the 

 sides in the directions indicated by the order of the letters; prove 

 that their resultant acts along the line joining the intersection of 

 AC, BD to the intersection of the tangents at B, D. 



In a triangular lamina ABC, AD, BE, CF are the per- 



pon.li.-uhirs, and forces BD, CD, CE, J /.'. .!/', ///' are applied to 

 iinina ; irove that their resultant passes through the centre 

 of the circumscribed circle. 



1-1 .">. Three r.jual forces P act at the angles of a triangle 

 ABC perpendicular [ -osite sides ; pn.\r that 



tlirir resultant is e.jual to 



A X . 

 -8 sin sin 



l-l 1 '.. If be tli-' Centre of tin- riivuniscrili-l riivlr, ami A 

 tlie centre of [ ikn "fa ferUUlglc .\1> ( \ tlin- CblOei : 



