CIRCULAR LOCI. 
Ill 
The conditions are 
n — n 
and a + a" = a' + a'", or a + a" = 2ît — (a + a'"). 
Lhuilier: EUmens d? Analyse Géométrique et d : Analyse 
Algébrique, p. 144. 
18. To find the locus of a point in the plane of a triangle, 
such that, if perpendiculars be drawn from it upon the directions 
of its sides, the area of the triangle, formed by straight lines 
joining the feet of the three perpendiculars, may be constant. 
If the equations to the three sides of the triangle be 
£ccosa + ?/ sina = 8, x cos a' + y sin a' = 8', x cos a" + y sin a" = 8", 
and Id be the constant area, the required locus will be two 
circles denoted by the double equation 
( 
sin (a"—a' 
± 2& 2 = (x 2 +y 2 ) sin a sin d sin a 
H ; 7 
sm a 
+ 8 sin (a' — a") {x cos (a + a" — a) + y sin (a' + a" — a)} 
+ 8' sin (a" — a) {x cos (a" + a — a) + y sin (a" + a — a')} 
+ 8" sin (a — a') [x cos (a + a' — a") + y sin (a + a' — a")} 
(sin (a — a') sin (a — a") sin (a" — a)) 
+ ôôè | ÿ +— l — + — f —p 
Querret : Gergonne, Annales de Mathématiques, tom. XIV. p. 280. 
Stunn : Ibid., tom. xiv. p. 286.