A) \[\sqrt{4{{c}^{2}}-2{{(a-b)}^{2}}}\]
B) \[\sqrt{4{{c}^{2}}+2{{(a-b)}^{2}}}\]
C) \[\sqrt{4{{c}^{2}}-2{{(a+b)}^{2}}}\]
D) \[\sqrt{4{{c}^{2}}+2{{(a+b)}^{2}}}\]
Correct Answer: A
Solution :
\[{{C}_{1}}(a,\ b),\ {{C}_{2}}(b,\ a),\ {{r}_{1}}={{r}_{2}}=c\] \[\therefore \]\[{{C}_{1}}P=\frac{1}{2}\sqrt{{{a}^{2}}+{{b}^{2}}+{{a}^{2}}+{{b}^{2}}-4ab}\] Length of common chord \[=2\text{ }{{\left[ {{c}^{2}}-\frac{1}{4}\left\{ 2({{a}^{2}}+{{b}^{2}})-4ab \right\} \right]}^{1/2}}\] \[=2\text{ }{{\left( \frac{2{{c}^{2}}-{{a}^{2}}-{{b}^{2}}+2ab}{2} \right)}^{1/2}}=\sqrt{4{{c}^{2}}-2{{(a-b)}^{2}}}\].You need to login to perform this action.
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