Mathematics - Circle Question with Solution | TestHub

Radical axis of the given circles is $x+5y-6=0$ which passes through $(1,1)$ Let the given circles intersect the circle

$$\begin{array}{rlrl}& x^2+y^2+2gx+2fy+c=0\text{ orthogonally then }2g(-3)+2f(-6)=c+1& & \end{array}$$

$$2g(-2)+2f(-1)=c-11$$

$$\Rightarrow 2g(-1)+2f(-5)=12\Rightarrow -g-5f-6=0$$

⇒ the radical axis passes through the centre $(-g,-f)$ of the third circle. Verify it does not pass through the mid-point of the line joining the centres.