If the chord of contact of tangents from a point on the circle $x^{2} + y^{2} = r_{1}^{2}$ to the circle $x^{2} + y^{2} = r_{2}^{2}$ touches the circle $x^{2} + y^{2} = r_{3}^{2}$, then $r_{,},\ r_{2},r_{3}$ are in

Question

Dr. Abubacker · Accepted Answer

(c)
Chord of contact of tangents at any point $P\left( x_{1},y_{1} ight)$ on the circle $x^{2} + y^{2} = r_{1}^{2}$ to the circle $x^{2} + y^{2} = r_{2}^{2}$ is $xx_{1} + yy_{1} = r_{2}^{2}$ which touches the circle $x^{2} + y^{2} = r_{3}^{2}$
$	herefore\ \ \ \frac{|0.x_{1} + 0.y_{1} - r_{2}^{2}|}{\sqrt{x_{1}^{2} + y_{1}^{2}}} = r_{3}$
$\Rightarrow \ \ \ r_{2}^{2} = r_{3}.\sqrt{x_{1}^{2} + y_{1}^{2}} = r_{3}.r_{1}\ \ \lbrack\because r_{1}^{2} = x_{1}^{2} + y_{1}^{2}brack$
So, $r_{1},r_{2},\ r_{3}$ are in GP

Q. If the chord of contact of tangents from a point on the circle $x^{2} + y^{2} = r_{1}^{2}$ to the circle $x^{2} + y^{2} = r_{2}^{2}$ touches the circle $x^{2} + y^{2} = r_{3}^{2}$, then $r_{,},\ r_{2},r_{3}$ are in

Explanation

Reviewed by Dr. Abubacker

Want more practice?