Question

The chord of contact of the 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:

• A. A.P.
• B. G.P.
• C. H.P.
• D. A.G.P.

Answer 1

The correct option is B

G.P.

Chord of contact of (acos$\theta$, asin$\theta$) w.r.t the circle

$x^2+y^2=b^{2}is\left(acos\theta \right)x+\left(asin\theta \right)y=b^2$

It is a tangent to then circle $x^2+y^2=c^2$

$c=\frac{b^2}{\sqrt{a^{2}co{s}^2\theta +a^{2}si{n}^2\theta }}\Rightarrow b^2=ac$