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 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.

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

Tangents are drawn from the points on the line x-y-5=0 ot x^(2)+4y^(2)=4 . Prove that all the chords of contanct pass through a fixed point

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

Tangents are drawn to x^(2)+y^(2)=1 from any arbitrary point P on the line 2x+y-4=0 .Prove that corresponding chords of contact pass through a fixed point and find that point.