A circle S cuts three circles aligned & x^2+y^2-4 x-2 y+4=0 & x^2+y^2-2 x-4 y+1=0 & and x^2+y^2+4 x+2 y+1=0 orthogonally. aligned Then, the radius of S is

Step-by-step solution

Let the circle aligned & S x^2+y^2+2 g x+2 f y+c=0 & x^2+y^2-4 x-2 y+4=0 & x^2+y^2-2 x-4 y+1=0 aligned and x^2+y^2+4 x+2 y+1=0 , respectively. aligned & 2 g(2)+2 f(1)=c+4 & 4 g+2 f=c+4... (i) & 2 g(1)+2 f(2)=c+1 & 2 g+4 f=c+1... (ii) aligned and 2 g(-2)+2 f(-1)=1+c -4 g-2 f=1+c... (iii) On solving eqs. (i), (ii) and (iii), we get g= 3 4 , f=- 3 4 , c=- 10 4 Equation of circle, S=x^2+y^2+ 3 2 x- 3 2 y- 10 4 =0 aligned & Radius = ( 3 4 )^2+ ( -3 4 )^2+ 10 4 & = 9 16 + 9 16 + 10 4 = 58 16 = 29 8 aligned