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.

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 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 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 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 family of circles passing through the points (3, 7) and (6, 5) cut the circle x^2 + y^2 - 4x-6y-3=0 . Show that the lines joining the intersection points pass through a fixed point and find the coordinates of the point.

Find the equation of a circle, which touches the line x+ y = 5 at the point (-2, 7) and cuts the circle x^2+ y^2+ 4x - 6y +9 =0 orthogonally.

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 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