JEE Main On 8 April 2017 Question 26
Question: If two parallel chords of the a circle, having diameter 4 units, lie on the opposite sides of the centre and subtend angles $ {{\cos }^{-1}}( \frac{1}{7} ) $ and $ {{\sec }^{-1}}(7) $ at the centre respectively, then the distance between these chords, is : [JEE Online 08-04-2017]
Options:
A) $ \frac{8}{\sqrt{7}} $
B) $ \frac{16}{7} $
C) $ \frac{4}{\sqrt{7}} $
D) $ \frac{8}{7} $
Show Answer
Answer:
Correct Answer: A
Solution:
- $ \cos 2Q=1/7 $ $ =2{{\cos }^{2}}Q-1=1/7 $ $ =2{{\cos }^{2}}Q=8/7 $ $ {{\cos }^{2}}Q=4/7 $ $ =\frac{cp^{2}}{4}=\frac{4}{7} $ $ =Cp=\frac{4}{\sqrt{7}} $ $ \sec 2Q=7 $ $ =\frac{2}{2{{\cos }^{2}}Q-1}=7 $ $ =2{{( \frac{Cp _2}{2} )}^{2}}-1=\frac{1}{7} $ $ =2{{( \frac{Cp _2}{2} )}^{2}}=\frac{8}{7} $ $ = $ $ \frac{4}{\sqrt{7}}+\frac{4}{\sqrt{7}}=\frac{8}{\sqrt{7}} $
