PLANE TRIGONOMETRY. 7 "> 



A The distances between the centre of the inscribed circle 

 and those of the escribed circles being respectively a', /8', y ; 

 prove that 



and that - 27? (a" + /T + y") + afty' = 0. 



353. Trove that 



and ^A 3 = (1 + cos A) (1 + cos B) (1 + cos <7> 



. Prove that 

 A D ^ @ V tt Bi y 



~ = 7T = c = ~~~T = "7j5" = ~ (7* 



cos- cos -- cos -jr- sin sin g sin ., 



~*. If 7, r be the radii of two of the four circles which 

 touch the sides of a triangle, and a. the distance between their 



centres, the area of the triangle will be qr */ / \~ 1 * uo 



upprr Hgn being taken when either of the circles is the inscril" ! 



356. 0, <y are the centres of tli<> circumscribed circle, and <>f 

 tip- inscribed or one of the escribed circles J', //', (" th' point^ 

 of contact of the latter circle with the sides, L the centre of per 

 pcmliculure of the triangle A'KC 1 '; prove that 0, (/, L are in one 

 straight line, and that 



<yi : Off :: r : JR, or :: r, : R, Ac. 

 7. If an isosceles triangle be constructed whose vert 

 angle is cos"'^, the inscribed circle will pass through the centre 

 !>' ii'licuhirs. 



