A) \[2\sqrt{{{a}^{2}}+{{b}^{2}}}\]
B) \[\frac{ab}{\sqrt{{{a}^{2}}+{{b}^{2}}}}\]
C) \[\frac{2ab}{\sqrt{{{a}^{2}}+{{b}^{2}}}}\]
D) None of these
Correct Answer: B
Solution :
Equation of common chord is\[ax-by=0\]. Now length of common chord \[=2\sqrt{r_{1}^{2}-p_{1}^{2}}=2\sqrt{r_{2}^{2}-p_{2}^{2}}\] where \[{{r}_{1}}\] and \[{{r}_{2}}\] are radii of given circles and \[{{p}_{1}},\ {{p}_{2}}\] are the perpendicular distances from centres of circles to common chords. Hence required length \[=2\sqrt{{{a}^{2}}-\frac{{{a}^{4}}}{{{a}^{2}}+{{b}^{2}}}}=\frac{2ab}{\sqrt{{{a}^{2}}+{{b}^{2}}}}\].
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