Question

A diameter of the circle $x^2+y^2=2x+6y-6$ is a chord of the another circle with centre $(2,1)$. The radius of this circle $C$ is $\left(inunits\right)$

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

Answer 1

The correct option is B $3$

Chords length $=2\sqrt{r^2-d^2}$ equation of circle is $(x-h{)}^2+(y-k{)}^2=r^2$

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

$(x^2-2x+1)+(y^2-6y+9)-1-10+4=0$

$(x-1{)}^2+(y-3{)}^2=4$

So $c=(1,3)$ and $r=2$

distance from center $(2,1)$ to chord of length $4$ is the equation of the chord can be $2x-4y+1=r^2$

This chord is diameter of second circle which means center $(1,3)$

$2\left(1\right)-4\left(3\right)+1=r^2$

$2-12+1=r^2$

$r=3$