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

(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.

(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 chord of contact of tangents from a point P (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 :

The polar of the line 8x-2y=11 with respect to the circle 2x^(2)+2y^(2)=11 is

The polar of the line 8x-2y=11 with respect to the circle 2x^(2)+2y^(2)=11 is

If the polars of points on the circle x^2+y^2=a^2 w.r.t. the circle x^2+y^2=b^2 touch the circle x^2+y^2=c^2 then a, b, c are in

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 . If the straight line touches the circle x^2+y^2=r^2 , then :

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.