Distances from the origin to the centres of the three circles

MATHEMATICS · Subjective · CBSE · Mathematics · Conic Sections · Conic Sections

Problem

Distances from the origin to the centres of the three circles x2+y2−2λx=c2x^2 + y^2 - 2\lambda x = c^2 , where cc is a constant and λ\lambda is available, are in GP. Prove that the lengths of tangents drawn from any point on the circle x2+y2=c2x^2 + y^2 = c^2 to the three circles are also in GP.

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