L62 .1 N -I/ > //' '/ "// //;> \ n 



Tlnvc circles. taken l\\n ami t\\, lia\o three radical axes 

 It is easily sli.\\n tliat these three radical axes p;i^s through 



a common point ; tins {mint is called the radical center of the 

 three circlet). 



EXERCISES 



1. Find the jiiatimi of the common chord of the cii 



z* + y ~ 3* - 5y - 8 = 0, x + y* + Sx = 0. 



2. Kind tin* points of intersection of tin- circles in exercise 1, and the 



<>f thi-ir common ci 



3. Fiml the radical axis, and also the length of the common clu.nl. 

 for t he circles X s + y* -f ax + by + c = 0, x* + y* + bx + ay + c = 0. 



4. Find the radical center of the three circles 



ar* + y 2 -f- 4* + 7 = 0, 

 ' 3 + y 2 ) + 3* + 5y + 9 = 0, 



** + y a -H y = 0. 



5. Show that tangents from the radical center, in exercise 4, to ill-- 

 three circles, respectively, are equal in length. 



6. Prove analytically that the tangents to two circles from any point 

 on ili'-ii radical axis are equal. 



7. Find th< polar of the radical center of the circles in exercise 4, 

 with respect to each circle. 



8. Prove analytically that the three radical axes of three circles, 



being taken in pairs, meet in a common point. 



98. The equation of a circle : polar coordinates. Let OR 



In- tin- initial line, the pole, C=(p v #,) tin- <-ntT <,f tin- 



circle, r its radius, and /'^(/3, 0) 

 any point >n tin- circle. l)ia\v 0(7, 

 OP, and OP ; then, by trigoii<um-t i \ . 



r 2 = /) 2 -f/) 1 2 -2/>/) 1 cos (0-0,), i.e., 



^-2^006(0-0,) 



+ , l _ f a SB o. . . . [39] 



which is the equation of the given 



