Orthogonality OF two circles

Find the equation to the circle orthogonal to the two circles x^(2)+y^(2)-4x6y+11=0;x^(2)+y^(2)-10x-4y+21=0 and has 2x+3y=7 as diameter.

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 .

radical axis,angle OF intersection,condition OF orthogonality||family OF circle

If centre of a circle lies on the line 2x - 6y + 9 =0 and it cuts the circle x^(2) + y^(2) = 2 orthogonally then the circle passes through two fixed points

If a circle Passes through point (1,2) and orthogonally cuts the circle x^(2)+y^(2)=4, Then the locus of the center is:

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

Consider the circle: x^2+y^2=r^2 with centre O. A and B are collinear with O such that OA. OB=r^2. The number of circles passing through A and B, which are orthogonal to the circle C is

Consider two circle x^(2)+y^(2)=1 and (x-1)^(2)+(y-1)^(2)=3 ,then the circle which is orthogonal to given circle may be