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

Question

Dr. Abubacker · Accepted Answer

(b)
Let the point on $x^{2} + y^{2} = a^{2}$ is $(a\cos	heta,\ a\sin	heta)$
Equation of chord of contact is
$ax\cos	heta + ay\sin	heta = b^{2}$
It touches circle $x^{2} + y^{2} = c^{2}$
$	herefore\ \left| \frac{- b^{2}}{\sqrt{a^{2}\cos^{2}	heta + a^{2}\sin^{2}	heta}} ight| = c$
$\Rightarrow b^{2} = ac$
$	herefore a,\ b,\ c$ are in GP

Q. If the chord of contact of tangents drawn from a point on the circle $x^{2} + y^{2} = a^{2}$ to the circle $x^{2} + y^{2} = b^{2}$ touches the circle $x^{2} + y^{2} = c^{2}$, then $a,\ b,c$ are in

Explanation

Reviewed by Dr. Abubacker

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