Prove that the radii of the circles `x^2 +y^2 = 4, 4x^2 + 4y^2 - 8x-24y+15=0 and x^2 + y^2 - 4y - 5 =0` are in arithmetic progression.

Prove that the radii of the circles x^(2)+y^(2)=1,x^(2)+y^(2)-2x-6y=6and x^(2)+y^(2)-4x-12y-9=0 are in arithmetic progression.

Prove that the radi of the circles x^(2)+y^(2)=1x^(2)+y^(2)-2x-6y=6 and x^(2)+y^(2)-4x-12y=9 are in arithmetic progression.

Two circles x^(2) + y^(2) - 2x - 4y = 0 and x^(2) + y^(2) - 8y - 4 = 0

Prove that the centres of the three circles : x^2 + y^2 -4x-6y-14=0, x^2 + y^2+ 2x+4y-5=0 and x^2 + y^2-10x -16y + 7 = 0 are collinear.

The point of tangency of the circles x^2+ y^2 - 2x-4y = 0 and x^2 + y^2-8y -4 = 0 , is

The point of tangency of the circles x^2+ y^2 - 2x-4y = 0 and x^2 + y^2-8y -4 = 0 , is

The point of tangency of the circles x^2+ y^2 - 2x-4y = 0 and x^2 + y^2-8y -4 = 0 , is

The radical axis of the circles x^(2) + y^(2) + 4x + 8y + 19 = 0 , x^(2) + y^(2) + 8x + 4y + 19 = 0 is

Two circles x^(2) + y^(2) - 4x + 10y + 20 = 0 and x^(2) + y^(2) + 8x - 6y - 24= 0

Prove that the centres of the circle x^(2) + y^(2) - 4x - 2y + 4 = 0, x^(2) + y^(2) - 2x - 4y + 1 = 0 and x^(2) + y^(2) + 2x - 8y + 1 = 0 are collinear. More over prove that their radii are in geometric pregression.