Find the length of the tangent drawn from any point on the circle `x^2+y^2+2gx+2fy+c_1=0` to the circle `x^2+y^2+2gx+2fy+c_2=0`

The length of the tangent from a point on the circle x^(2)+y^(2)+4x-6y-12=0 to the circle x^(2)+y^(2)+4x-6y+4=0 is

The lengths of the tangents from any point on the circle x^(2)+y^(2)+8x+1=0 to the circles x^(2)+y^(2)+7x+1=0 and x^(2)+y^(2)+4x+1=0 are in the ratio

If the length of the tangent drawn from (f, g) to the circle x^2+y^2= 6 be twice the length of the tangent drawn from the same point to the circle x^2 + y^2 + 3 (x + y) = 0 then show that g^2 +f^2 + 4g + 4f+ 2 = 0 .

The length of the tangent from (0, 0) to the circle 2(x^(2)+y^(2))+x-y+5=0 , is

Tangents drawn from (2, 0) to the circle x^2 + y^2 = 1 touch the circle at A and B Then.

Find the angle between the pair of tangents drawn from (0,0) to the circle x^(2) + y^(2) - 14 x + 2y + 25 = 0.

Length of the tangent. Prove that the length t o f the tangent from the point P (x_(1), y(1)) to the circle x^(2) div y^(2) div 2gx div 2fy div c = 0 is given by t=sqrt(x_(1)^(2)+y_(1)^(2)+2gx_(1)+2fy_(1)+c) Hence, find the length of the tangent (i) to the circle x^(2) + y^(2) -2x-3y-1 = 0 from the origin, (2,5) (ii) to the circle x^(2)+y^(2)-6x+18y+4=-0 from the origin (iii) to the circle 3x^(2) + 3y^(2)- 7x - 6y = 12 from the point (6, -7) (iv) to the circle x^(2) + y^(2) - 4 y - 5 = 0 from the point (4, 5).

If the distances from the origin of the centers of three circles x^2+y^2+2lambdax-c^2=0,(i=1,2,3), are in GP, then prove that the lengths of the tangents drawn to them from any point on the circle x^2+y^2=c^2 are in GP.

Find the centre and radius of the circle ax^(2) + ay^(2) + 2gx + 2fy + c = 0 where a ne 0 .

The length of the chord of contact of the tangents drawn from the point (-2,3) to the circle x^2+y^2-4x-6y+12=0 is: