question_answer

Three circles of radii a, b, c (a < b < c) touch each other externally. If they have x-axis as a  common tangent, then: [JEE Main Online Paper (Held On 09-Jan-2019 Morning]

A) \[\frac{1}{\sqrt{b}}\,\,=\,\,\frac{1}{\sqrt{a}}+\frac{1}{\sqrt{c}}\,\]

B) a, b, c are in A. P.

C) \[\sqrt{a},\,\,\sqrt{b},\,\,\sqrt{c}\,\,are\,\,in\,\,A.P.\]

D) \[\frac{1}{\sqrt{a}}=\frac{1}{\sqrt{b}}+\frac{1}{\sqrt{c}}\]   

Correct Answer: D

Solution :

\[AB=AC+CB\] \[\sqrt{{{(b+c)}^{2}}\,+\,{{(b-c)}^{2}}}\,\,\,=\,\,\,\sqrt{{{(b-a)}^{2}}\,-\,{{(b-a)}^{2}}\,+}\] \[\sqrt{{{(a+c)}^{2}}\,-\,{{(a-c)}^{2}}}\,\,\,\] Solve \[\frac{1}{\sqrt{a}}\,\,=\,\,\frac{1}{\sqrt{b}}\,\,=\,\,\frac{1}{\sqrt{c}}\,\]