Conic-Sections Question 562
Question: Consider a circle of radius R. what is the length of a chord which subtends an angle $ \theta $ at the centre?
Options:
A) $ 2R\sin ( \frac{\theta }{2} ) $
B) $ 2R\sin \theta $
C) $ 2R\tan ( \frac{\theta }{2} ) $
D) $ 2R\tan \theta $
Show Answer
Answer:
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}. $
BETA
