Question

If common chord of the circle $C$ with centre at $(2,1)$ and radius $r$ and the circle $x^2+y^2-2x-6y+6=0$ is a diameter of the second circle, then value of $r$ is

• A. $3$
• B. $2$
• C. $3/2$
• D. $1$

Answer 1

The correct option is A $3$

Equation of the circle $C$ is $(x-2{)}^2+(y-1{)}^2=r^2$

$\Rightarrow x^2+y^2-4x-2y+5-r^2=0$

Equation of the common chord is $(x^2+y^2-4x-2y+5-r^2)-(x^2+y^2-2x-6y+6)=0$
$\Rightarrow 2x-4y+r^2+1=0$

If it is a diameter of the second circle, it passes through the centre $(1,3)$ of the circle So $2-4\times 3+r^2+1=0$

$\Rightarrow r^2=9$

$\Rightarrow r=3$