The radius of a circle whose center is (2,1) and one of the chords is a diameter of the circle x^2+y^2-2 x-6 y+6=0 , is units.

Step-by-step solution

Let (x₁, y₁ ) and (x₂, y₂ ) be end point of diameter of circle, then equation of circle be (x-x₁ ) (x-x₂ )+ (y-y₁ ) (y-y₂ )=0 Given, equation of circle is aligned & x^2+y^2-2 x-6 y+6=0 & x^2-2 x+1+y^2-6 y+5=0 & (x-1)^2+(y-1)(y-5)=0 & (x-1)(x-1)+(y-1)(y-5)=0 & aligned Compare Eqs. (i) and (ii), we obtain end points of diameter be (1,1) and (1,5) . Now, we have to find radius of circle having centre at (2,1) and one of its chord having end point (1,1) and (1,5) From given circle, aligned x^2+y^2 & =r^2 x= (2-1)^2+(1-