Prove that the centres of the circles `x^2+y^2=1`, `x^2+y^2+6x-2y-1=0` and `x^2+y^2-12x+4y=1` are collinear

Prove that the centres of the three circles (x^2 +y^2 −4x−6y−12=0) , (x^2 +y^2 +2x+4y−5=0) and (x^2 +y^2 −10x−16y+7=0) are collinear.

The circles x^2 + y^2 + 6x + 6y = 0 and x^2 + y^2 - 12x - 12y = 0

Prove that the radii of the circles x^(2)+y^(2)=1,x^(2)+y^(2)-2x-6y=6andx^(2)+y^(2)-4x-12y=9 are in AP.

The radical centre of the circles x^2+y^2=9, x^2+y^2-2x-2y-5=0 , x^2+y^2+4x+6y-19=0 is

Prove that the centres of the three circles x^2 + y^2 - 4x – 6y – 12 = 0,x^2+y^2 + 2x + 4y -5 = 0 and x^2 + y^2 - 10x – 16y +7 = 0 are collinear.

Coordinates of the centre of the circle which bisects the circumferences of the circles x^2 + y^2 = 1; x^2 + y^2 + 2x - 3 = 0 and x^2 + y^2 + 2y-3 = 0 is

Find the equation of the circle the end points of whose diameter are the centres of the circle : x^2 + y^2 + 6x - 14y=1 and x^2 + y^2 - 4x + 10y=2 .

The circles x^(2)+y^(2)-2x-4y+1=0 and x^(2)+y^(2)+4y+4x-1 =0

Find the number of common tangents of the circles x^2+y^2-2x-6y+9=0 and x^2+y^2+6x-2y+1=0

Find the radical centre of the following circles x^2+y^2-4x-6y+5=0 x^2+y^2-2x-4y-1=0 x^2+y^2-6x-2y=0