THE IH-AJ\T)-CIECHMSCEIBED POLYGON. 
239 
xAnd if this be a point of the circumscribed circle 
— V+(V— 2^7— /")4-2Lf\/ V— V=0, 
that is, 
2{'L—l)i\/ V=^"+V, 
or 
(r4-V)"+4(L-^)^V=0, 
•which is the required relation : but to express it in terms of the ordinary data R, r, a, 
the equations of the circles, putting therein z=\, become 
and therefore 
these equations give 
and thence 
{x-l )^+/ = V + P, 
(^-L)"+3/" = V+P, 
a =L — Z, 
ri =V+P, 
R"=V + L"; 
a 
a 
=L+?, 
= L-^; 
-L'— o ’ 
2a 
and 
V=R"- 
if with iNI. iNlEXTiox we write 
. (2a^R^+ 2aV"+ 2rill^- R^-r^- 
The equation 
thus becomes 
1 {r^ + _ 2riR2 _ - 2RV) = - v. 
(^^+V)^+4(L-0^ V = 0 
that is, it becomes ('-1-1 = 0, which is the other factor of the complete condition 
?(v+l) = 0. 
