If `C_1,C_2,a n dC_3` belong to a family of circles through the points `(x_1,y_2)a n d(x_2, y_2)` prove that the ratio of the length of the tangents from any point on `C_1` to the circles `C_2a n dC_3` is constant.

If C_(1),C_(2), and C_(3) belong to a family of circles through the points (x_(1),y_(2)) and (x_(2),y_(2)) prove that the ratio of the length of the tangents from any point on C_(1) to the circles C_(2) and C_(3) is constant.

If the distances from the origin of the centers of three circles x^2+y^2+2lambdax-c^2=0,(i=1,2,3), are in GP, then prove that the lengths of the tangents drawn to them from any point on the circle x^2+y^2=c^2 are in GP.

If the distances from the origin of the centers of three circles x^2+y^2+2lambdax-c^2=0,(i=1,2,3), are in GP, then prove that the lengths of the tangents drawn to them from any point on the circle x^2+y^2=c^2 are in GP.

if the distances from the origin to the centre of three circles x^2+y^2+2lambda_ix-c^2=0(i=1,2,3) are in G.P. ,then the lengths of the tangents drawn to them from any point on the circle x^2+y^2=c^2 are in

If the distances from the origin of the centers of three circles x^(2)+y^(2)+2 lambda x-c^(2)=0,(i=1,2,3), are in GP,then prove that the lengths of the tangents drawn to them from any point on the circle x^(2)+y^(2)=c^(2) are in GP.

If the distances from the origin to the centres of three circles x^(2)+y^(2)-2kix=c^(2), (i=1,2,3) are in G.P, then the length of the tangents drawn to them from any point on the circle x^(2)+y^(2)=c^(2)" are in "

If the distances from the origin to the centres of the three circles x^2+ y^2-2 lamda x= c^2 , where c is constant and lamda is variable, are in G.P., prove that the lengths of tangents drawn from any point on the circle x^2 +y^2= c^2 to the three circles are also in GP.

The chords of contact of tangents from three points A ,Ba n dC to the circle x^2+y^2=a^2 are concurrent. Then A ,B a n dC will be