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.

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 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

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

(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.

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

The chords of contact of the pair of tangents drawn from each point on the line 2x + y=4 to the circle x^2 + y^2=1 pass through the point (h,k) then 4(h+k) is

If the chord of contact of the tangents drawn from the point (h , k) to the circle x^2+y^2=a^2 subtends a right angle at the center, then prove that h^2+k^2=2a^2dot

Tangents drawn from a point on the circle x^2+y^2=9 to the hyperbola x^2/25-y^2/16=1, then tangents are at angle