A) \[\sqrt{\frac{{{r}^{2}}({{a}^{2}}+{{b}^{2}})-{{a}^{2}}{{b}^{2}}}{{{a}^{2}}+{{b}^{2}}}}\]
B) \[2\sqrt{\frac{{{r}^{2}}({{a}^{2}}+{{b}^{2}})-{{a}^{2}}{{b}^{2}}}{{{a}^{2}}+{{b}^{2}}}}\]
C) \[2\frac{\sqrt{{{r}^{2}}({{a}^{2}}+{{b}^{2}})-{{a}^{2}}{{b}^{2}}}}{{{a}^{2}}+{{b}^{2}}}\]
D) None of these
Correct Answer: B
Solution :
[b] Length of chord \[=2{{\{{{(radius)}^{2}}-{{(length\,\,of\bot from\,\,centre\,\,of\,\,chord)}^{2}}\}}^{1/2}}\]\[=2{{\left\{ {{r}^{2}}-{{\left( \frac{-1}{\sqrt{(1/{{a}^{2}})+(1/{{b}^{2}})}} \right)}^{2}} \right\}}^{1/2}}\] \[=2\sqrt{\frac{{{r}^{2}}({{a}^{2}}+{{b}^{2}})-{{a}^{2}}{{b}^{2}}}{{{a}^{2}}+{{b}^{2}}}}\]
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