JEE Mains · Maths · STD 11 - 10.1 circle and system of circle
If two parallel chords of a circle, having diameter \(4\, units\), lie on the opposite sides of the centre and subtend angles \({\cos ^{ - 1}}\left( {\frac{1}{7}} \right)\) and \({\sec ^{ - 1}}\left( 7 \right)\) at the centre respectively, then the distance between these chords, is
- A \(\frac{4}{{\sqrt 7 }}\)
- B \(\frac{8}{{\sqrt 7 }}\)
- C \(\frac{8}{7}\)
- D \(\frac{16}{7}\)
Answer & Solution
Correct Answer
(B) \(\frac{8}{{\sqrt 7 }}\)
Step-by-step Solution
Detailed explanation
Sine \(\cos \,2\theta = 1/7 \Rightarrow 2{\cos ^2}\theta - 1 = 1/7\) \( \Rightarrow 2{\cos ^2}\theta = 8/7\) \( \Rightarrow {\cos ^2}\theta = 4/7\) \( \Rightarrow {\cos ^2}\theta = \frac{4}{7}\) \( \Rightarrow {\cos ^2}\theta = \frac{2}{{\sqrt 7 }}\) Also,…
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