A) \[2R\sin \left( \frac{\theta }{2} \right)\]
B) \[2R\sin \theta \]
C) \[2R\tan \left( \frac{\theta }{2} \right)\]
D) \[2R\tan \theta \]
Correct Answer: A
Solution :
[a] Let there be a circle of radius R and AB a chord. \[OD\bot AB\] and \[AD=DB.\] And \[AD=2AD\] \[\angle AOB=\theta \] \[\Rightarrow \angle AOD=\frac{\theta }{2}\] In \[\Delta AOD,\] \[\sin \frac{\theta }{2}=\frac{AD}{OA}\] \[\sin \frac{\theta }{2}=\frac{AD}{R}\] \[AD=R\sin \frac{\theta }{2}\] \[\therefore \] Length of chord \[AB=2AD=2R\sin \frac{\theta }{2}.\]You need to login to perform this action.
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