THE APPLICATION OF ALGEBRA 
From the same equations the problem may be re 
solved, when' the distances from the three angular 
points to the circumference of the. inscribed circle are 
given: for, denoting the said distances by f, g, and h, 
you will have AO — x 4- f, BOz: x -I g, and CO—a: 
+ h ; which values being wrote in the room of a, b, 
and c, there wi 11 arise an equation of six dimensions : 
by means whereof x may be found. 
problem xxx. 
To draw a line NM to touch a circle D, given in mag 
nitude and position, so that the part thereof AC, inter 
cepted by two other lines BK, BL, given in position, shall 
be of a given length, 
Suppose CP and DE to be perpendicular to AB, and 
DF and DG to AC and PC, respectively; and let DA 
DC, and DP be drawn; putting DE — a, DF = 6, 
AC — c, BE — d, PC r x, PA rr y, and the tan 
gent of the given angle BCP, to the radius l, — t. 
Then, by trigonometry, l : t :: x : tx — BP; there 
fore DG (— PE) — d — tx; which, multiplied by 
v,u t —, give» , for the area of the tri- 
2 *2 
angle CDP: in like manner the area of the triangle 
PDA will be found — ; and that of ADC — ; 
2 2