A) \[\frac{{{A}_{1}}+{{A}_{2}}}{2}\]
B) \[{{\left[ \frac{1}{{{A}_{1}}}+\frac{1}{{{A}_{2}}} \right]}^{-1}}\]
C) \[\sqrt{{{A}_{1}}{{A}_{2}}}\]
D) \[{{\left[ \frac{\sqrt{{{A}_{1}}}+\sqrt{{{A}_{2}}}}{2} \right]}^{2}}\]
Correct Answer: C
Solution :
\[{{m}_{1}}=\frac{{{A}_{1}}}{O}\]and \[{{m}_{2}}=\frac{{{A}_{2}}}{O}\] \[\Rightarrow {{m}_{1}}{{m}_{2}}=\frac{{{A}_{1}}{{A}_{2}}}{{{O}_{2}}}\] Also it can be proved that \[{{m}_{1}}{{m}_{2}}=1\] So \[O=\sqrt{{{A}_{1}}{{A}_{2}}}\]
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