Find the center of the smallest circle which cuts circles `x^2+y^2=1` and `x^2+y^2+8x+8y-33=0` orthogonally.

Find the locus of the centres of the circle which cut the circles x^2+y^2+4x-6y+9=0 and x^2+y^2-5x+4y-2=0 orthogonally

The centre of the smallest circle touching the circles x^2+ y^2-2y -3=0 and x^2 +y^ 2-8x -18y +93= 0 is:

The equation of a circle is x^2+y^2=4. Find the center of the smallest circle touching the circle and the line x+y=5sqrt(2)

Find the coordinates of the point at which the circles x^2-y^2-4x-2y+4=0 and x^2+y^2-12 x-8y+36=0 touch each other. Also, find equations of common tangents touching the circles the distinct points.

Equation of the circle which cuts the circle x^2+y^2+2x+ 4y -4=0 and the lines xy -2x -y+2=0 orthogonally, is

Find the angle at which the circles x^2+y^2+x+y=0 and x^2+y^2+x-y=0 intersect.

The length of the common chord of the two circles x^2+y^2-4y=0 and x^2+y^2-8x-4y+11=0 is

Find the equation of a circle with center (4, 3) touching the circle x^2+y^2=1

Find the equation of the circle which cuts the three circles x^2+y^2-3x-6y+14=0,x^2+y^2-x-4y+8=0, and x^2+y^2+2x-6y+9=0 orthogonally.

Find the centre and the radius of the circle x^(2)+y^(2)+8x+10y-8=0 .