If the chord of contact of the tangents drawn from a point on the circle `x^2+y^2+y^2=a^2` to the circle `x^2+y^2=b^2` touches the circle `x^2+y^2=c^2` , then prove that `a ,b` and `c` are in GP.

chord of contact of the tangents drawn from a point on the circle x^(2)+y^(2)=81 to the circle x^(2)+y^(2)=b^(2) touches the circle x^(2)+y^(2)=16 , then the value of b is

If the chord of contact of the tangents from a point on the circle x^2 + y^2 = a^2 to the circle x^2 + y^2 = b^2 touch the circle x^2 +y^2 = c^2 , then the roots of the equation ax^2 + 2bx + c = 0 are necessarily. (A) imaginary (B) real and equal (C) real and unequal (D) rational

The chord of the contact of tangents drawn from a point on the circle x^(2) + y^(2) = a^(2) to the circle x^(2) = y^(2) = b^(2) touches the circle x^(2) + y^(2) =c^(2) such that b^(m)= a^(n)c^(p) , where m,n p in N and m,n,p are prime to each other , then the value of m+ n+ p -3 is :

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:

If the chord of contact of tangents from a point P(h, k) to the circle x^(2)+y^(2)=a^(2) touches the circle x^(2)+(y-a)^(2)=a^(2) , then locus of P is

The angle between the tangents drawn from a point on the director circle x^(2)+y^(2)=50 to the circle x^(2)+y^(2)=25 , is

If two tangents are drawn from a point to the circle x^(2) + y^(2) =32 to the circle x^(2) + y^(2) = 16 , then the angle between the tangents is

If the chord of contact of tangents from a point (x_(1),y_(1)) to the circle x^(2)+y^(2)=a^(2) touches the circle (x-a)^(2)+y^(2)=a^(2), then the locus of (x_(1),y_(1)) is