Question

If a diameter of the circle $x^2+y^2-2x-6y+6=0$ is a chord of another circle $C$ having centre $(2,1)$, then the radius of the circle $C$ is

• A. $2$
• B. $\sqrt{3}$
• C. $3$
• D. $\sqrt{5}$
• E. $5$

Answer 1

Answer: (C)

$3$

Given equation of circle is

$x^2+y^2-2x-6y+6=0$

compare this equation with

$x^2+y^2+2gx+2fy+c=0$

we get

$\therefore$ Centre$g=-1,f=-3$

and $c=6=(-g,-f)=(1,3)$

distance $\left(d\right)=AB=\sqrt{{(1-2)}^2+{(3-1)}^2}=\sqrt{1+4}=\sqrt{5}$

$\therefore r_1=\sqrt{g^2+f^2-c}=\sqrt{1+9-6}=2$

Hence radius of another circle

$r_2=\sqrt{{r_1}^2+d^2}=\sqrt{5+4}=3$