Three circles of radii a, b, c

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Question:

Three circles of radii a, b, c $(a

$\frac{1}{\sqrt{\mathrm{a}}}=\frac{1}{\sqrt{\mathrm{b}}}+\frac{1}{\sqrt{\mathrm{c}}}$
a, b, c are in A. P.
$\sqrt{\mathrm{a}}, \sqrt{\mathrm{b}}, \sqrt{\mathrm{c}}$ are in A. P.
$\frac{1}{\sqrt{b}}=\frac{1}{\sqrt{a}}+\frac{1}{\sqrt{c}}$

Correct Option: 1

Solution:

$\mathrm{AB}=\mathrm{AC}+\mathrm{CB}$

$\sqrt{(b+c)^{2}-(b-c)^{2}}$

$=\sqrt{(b+a)^{2}-(b-a)^{2}}+\sqrt{(a+c)^{2}-(a-c)^{2}}$

$\sqrt{b c}=\sqrt{a b}+\sqrt{a c}$

$\frac{1}{\sqrt{a}}=\frac{1}{\sqrt{c}}+\frac{1}{\sqrt{b}}$