/// 



To .!.:..!. tii.- .- pi :.., <>f t)i common chord of two givon circles r 



. necessary to eliminate the term* in r 1 and jr s between their 

 equation*. /.';. to find the common chord of the circle* 



5y- OsO, 



6** + Gf* + 11 x f l.Jy-:M () 



in ult iply equation (a) ly 9 and subtract the result from equation (/?); 



r+*t 



< equation of the commo: f the given circle*. 



may be verified by finding tin- |.inu of t.- ruction 

 :-cles (a) and (ft), and then writing th- r.iu.t(ion of 

 the straight line through thoee two p. 



oe the common chord of two circles intersects each of these circles 

 in tt they intersect each other, therefore the points 



of two circles may be fomi-1 I 



i. mot, ,-!,., 1. 1 intersects either of t I the 



ks in which the circles (a) and (ft) intersect ea it ia only 



necessary to find the points in which (y) cuts either (a) or (ft). 



97. Radical axis; radical center. Tin- lino whoHo tMju.it ion 

 ued by eliminating tlu j? and y~ l>etwecn tli- 



uations of t\vt> gi .is in Art. 1H3, whether the 



U*s intersect in real points or not, is called the radical axis 



I.- two riivlrs. If tin* twn u r i\''' riivli-*; intn->rrt each 

 r in iva . thru this lino is also called their com- 



: that i-, the roninmn fhnr.l of lea is a 



case of th. r.idical axis in lea. 



iiion (3) of Art. 95, which for every value of * represents a 

 through the two points in which the given circles (1) and (2) inter- 

 may be written in the form 



coordinates of the center of this circle are (Art 79) 



g. + *0. * P* + *F* 



\+k I +* 



( be made to approach -1, both of these coordinates approach 

 hut the circle always passes through the two fixed points in which 

 given circles intersect , hence the common chord of two given ctata 

 be regarded as an large circle whose center is at infinity. 



liOM. 11 



