Mathematics - Circle Question with Solution | TestHub

Here, equation of tangent on $C_1$ at $(2,1)$ is: $2x+y-(x+2)-1=0$ Or $x+y=3$ If it cuts off the chord of the circle $C_2$ then the equation of the chord is: $$x+y=3$$ $\therefore$ distance of the chord from $(3,-2)$ is : $$d=\left|\frac{3-2-3}{\sqrt{2}}\right|=\sqrt{2}$$ Also, length of the chord is $l=4$ $$\begin{array}{rl}\therefore \text{ radius of }{C}_2=r& =\sqrt{{\left(\frac{l}{2}\right)}^2+d^2}\\ & =\sqrt{(2{)}^2+(\sqrt{2}{)}^2}=\sqrt{6}\end{array}$$