A) \[\sqrt{2}\] units
B) 1 unit
C) 2 units
D) \[\sqrt{3}\] units
Correct Answer: D
Solution :
We have given, \[{{A}_{1}},{{A}_{2}},\,{{A}_{1}}+{{A}_{2}}\] are in A.P. \[\Rightarrow \] \[2{{A}_{2}}={{A}_{1}}+{{A}_{1}}+{{A}_{2}}\,\,\Rightarrow \,\,{{A}_{2}}=2{{A}_{1}}\] ?.. (i) And \[{{A}_{2}}+{{A}_{1}}=\pi {{(3)}^{2}}\Rightarrow 3{{A}_{1}}=9\pi \]...(using (i) \[\Rightarrow \] \[{{A}_{1}}=3\pi \,\,\Rightarrow \,\,\pi r_{1}^{2}=3\pi \] [Here y, is the radius of smaller circle.] \[\Rightarrow \] \[{{r}_{1}}=\sqrt{3}\] units
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