A) \[\sqrt{{{a}^{2}}-{{b}^{2}}}\]
B) \[2\sqrt{{{a}^{2}}-{{b}^{2}}}\]
C) \[\sqrt{{{a}^{2}}+{{b}^{2}}}\]
D) \[2\sqrt{{{a}^{2}}+{{b}^{2}}}\]
Correct Answer: B
Solution :
In figure, AB is a chord of circle \[{{C}_{1}}\]which is a tangent to \[{{C}_{2}}\]. Since, tangent is perpendicular to radius through point of contact \[\therefore \] \[\angle OCA={{90}^{o}}\Rightarrow OA=a,\,\,OC=b\] In \[\Delta \,OCA,\] \[{{(OA)}^{2}}={{(OC)}^{2}}+{{(AC)}^{2}}\] \[\Rightarrow \] \[{{a}^{2}}={{b}^{2}}+{{(AC)}^{2}}\Rightarrow AC=\sqrt{{{a}^{2}}-{{b}^{2}}}\] \[\therefore \] Length of chord \[AB=2AC=2\sqrt{{{a}^{2}}-{{b}^{2}}}.\]You need to login to perform this action.
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