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If the chord of contact of tangent drawn from a point on the circle \( \Large x^{2}+y^{2}=a^{2} \) to the circle \( \Large x^{2}+y^{2}=b^{2} \) touches the circle \( \Large x^{2}+y^{2}=c^{2} \) then a, b, c are in

A) AP
B) GP
C) HP
D) none of these

Correct Answer:


B) GP

Description for Correct answer:
Let the point on \( \Large x^{2}+y^{2}=a^{2}\ is\ \left( \alpha \cos \theta,\ \alpha \sin \theta \right) \)

Equation of chord of contact is

\( \Large ax \cos \theta + ay \sin \theta = b^{2} \)

It touches circles \( \Large x^{2}+y^{2}=c^{2} \)

\( \Large \frac{-b^{2}}{\sqrt{a^{2}\cos^{2} \theta +a^{2}\sin^{2}\theta}}=c => b^{2} = ac \)

Therefore, a, b, c are in G.P.

Part of solved Circles questions and answers : >> Elementary Mathematics >> Circles

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