Question

The radius of the circle having centre at $(2,1)$ whose one of the chord is a diameter of the circle $x^2+y^2-2x-6y+6=0$

• A. $3$
• B. $2$
• C. $1$
• D. $\sqrt{3}$

Answer 1

The correct option is C $1$

Chord $AB$ is s a diameter of $x^2+y^2-2x-6y+6=0$
So, $AB=2r=2\times \sqrt{1^2+3^2-6}=4$
Center of $AB$ is a centre of a circle of $x^2+y^2-2x-6y+6=0$
Centre $=(1,3)$
By property, perpendicular from center of $AB$ is center of circle on any chord bisects the chord.
$\therefore AP=\frac{AB}{2}=2$
In $\Delta OPA,$ we have
$\Rightarrow O{P}^2+A{P}^2=O{A}^2$
$\Rightarrow 5+4=O{A}^2$
$\Rightarrow OA=3$
Radius of circle having centre $(2,1)$ is $OA$.
$\Rightarrow OA=3$ units