If a circle cuts orthogonally three circles, `S_1 = 0, S_2=0, S_3=0`, prove that it cuts orthogonally and circle `kS_1 + lS_2 + mS_3 = 0`.

If a circle S intersects circles S_1 and S_2 orthogonally. Prove that the centre of S lies on the radical axis of S_1 and S_2 .

The circle orthogonal to the three circles x^2+y^2+a_i x +b_i y+c=0 , (i=1,2,3) is

The circle orthogonal to the three circles x^2+y^2+a_i x +b_i y+c=0 , (i=1,2,3) is

The circleS orthogonal to three circleS x^(2)+y^(2)+a_(i) x+b_(i) y+c=0, i=1,2,3, is

All those circles which pass through (2,0) and (-2,0) are orthogonal to the circle (s)

If the circles of same radius a and centres (2,3), (5,6) cut orthogonally , then a=

Find the equation of the circle which cuts orthogonally the circle x^2 + y^2 – 6x + 4y -3 = 0 ,passes through (3,0) and touches the axis of y.

Find the equation of the circle which cuts orthogonally the circle x^2 + y^2 – 6x + 4y -3 = 0 ,passes through (3,0) and touches the axis of y.

The centre of the circle S = 0 lies on the line 2x -2y + 9 = 0 and S = 0 cuts orthogonally the circle x^2 + y^2 = 4 . Show that S = 0 passes through two fixed points and also find the co-ordinates of these two points.

If the circles of same radius a and centre (2, - 3), (-4, 5) cut orthogonally , then a =