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 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.

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 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 chord of contact of the tangent drawn from the point (a,b) to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 touches the circle x^(2)+y^(2)=k^(2), then find the locus of the point (a,b).

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

Ifchord ofcontact ofthe tangents drawn from the point (alpha,beta) to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 touches the circle x^(2)+y^(2)=c^(2), then the locus of the point