(prove that) If the polar of the points on the circle
`x^(2) + y ^(2) = a^(2)` with respect to the circle
` x^(2) + y^(2) = b^(2)` touches the circle `x^(2) + y^(2) = c^(2) `
then prove that a, b, c, are in Geometrical
progression.

If the polar of a point (p,q) with respect to the circle x^2 +y^2=a^2 touches the circle (x-c)^2 + (y-d)^2 =b^2 , then

If the pole of a straight line with respect to the circle x^(2)+y^(2)=a^(2) lies on the circle x^(2)+y^(2)=9a^(2) , then the straight line touches the circle

If the chord of contact of the 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 , then prove that a ,b and c are in GP.

The locus of poles of tangents to the circle (x-p)^(2)+y^(2)=b^(2) w.r.t. the circle x^(2)+y^(2)=a^(2) is

If the circle x^(2)+y^(2)+2ax=0, a in R touches the parabola y^(2)=4x , them

If the pole of the line with respect to the circle x^(2)+y^(2)=c^(2) lies on the circle x^(2)+y^(2)=9c^(2) then the line is a tangent to the circle with centre origin 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

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

If the line l x+m y-1=0 touches the circle x^2+y^2=a^2 , then prove that (l , m) lies on a circle.

If the line l x+m y-1=0 touches the circle x^2+y^2=a^2 , then prove that (l , m) lies on a circle.