A variable circle which always touches the line `x+2y-3=0` at (1, 1) cuts the circle `x^2+y^2+4x-2y+1=0` . then all common chords of cricles pass through a fixed point(P,Q). THEN P+Q=

A variable circle which always touches the line x+y-2=0 at (1,1) cuts the circle x^(2)+y^(2)+4x+5y-6=0. Prove that all the common chords of intersection pass through a fixed point.Find that points.

The radius of the circle which touches the line x+y=0 at M(-1,1) and cuts the circle x^(2)+y^(2)+6x-4y+18=0 orthogonally,is

A circle touching the line x +y - 2 = 0 at (1,1) and cuts the circle x^(2) +y^(2) +4x +5y - 6 = 0 at P and Q. Then

A variable circle always touches the line y-x=0 and passes though the point (0,0), the common chords of above cirlce and x^2+y^2+6x+8y-7=0 will pass through fixed point , whose coordinates are

Consider a family of circles passing through the point (3,7) and (6,5). Answer the following questions. If each circle in the family cuts the circle x^(2)+y^(2)-4x-6y-3=0 , then all the common chords pass through the fixed point which is

The equation of the cirele which passes through the point (1,1) and touches the circle x^(2)+y^(2)+4x-6y-3=0 at the point (2,3) on it is

If circle C passing through the point (2, 2) touches the circle x^2 + y^2 + 4x - 6y = 0 externally at the point (1, 1), then the radius of C is: