Discussion Forum

If  one of the diameters of the circle $x^{2}+y^{2}-2x-6y+6=0$   is a chord to the circle with centre (2,1), then the radius of the bigger circle is 

Answer:

Explanation:

Equation of circle 

$x^{2}+y^{2}-2x-6y+6=0$  

Centre (1,3)   ,r= $\sqrt{1+9-6}=2$

OA =   $\sqrt{(2-1)^{2}+(1-3)^{2}}\Rightarrow OA=\sqrt{1+4}=\sqrt{5}$

$\because$   AB= r=2    and $R^{2}=r^{2}+OA^{2}$

$\Rightarrow$      $R^{2}=4+5  \Rightarrow$    R=3