If the distances from origin of the centres of 3 circles x^{2}+y^{2}+2alphaix= a^{2 }(i=1,2,3) are in G.P. , then length of the tangents drawn to them frm any point on the circles x2+y2 = a2 are in :(a) A.P (b) G.P (c) H.P (d) None of theseAns) Ccentres of the 3 circles are (-alphai,0) (i= 1,2,3)Distances of thes from origin are alpha1, alpha2, alpha 3now (alpha2)^2= (alpha1)(alpha3)Also general point on x^{2}+y^{2}=a^{2} is (a costheta, a sintheta) length of tangent from this point on the given circle issqrt( (a cos theta)2+(a sintheta)2 +2alphai(a costheta) -a2)) = sqrt ( 2alphai(a costheta))now as alpha 1, alpha 2, alpha 3 are in GPthen sqrt alpha 1, sqrt alpha 2, sqrt alpha 3 are in gp then sqrt 2acos theta alpha 1 , 2acos theta alpha 2 and sqrt 2acos theta alpha 3 are also in GP