If the distances from the origin of the centers of three circles $x^{2} + y^{2} + 2 λ x - c^{2} = 0, (i = 1, 2, 3),$ 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.

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If the distances from the origin of the centers of three circles

x^{2} + y^{2} + 2 λ 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.

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Question Text

If the distances from the origin of the centers of three circles

x^{2} + y^{2} + 2 λ 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.

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