JEE Main 2017MathematicsCircleHardMCQ

JEE Main 2017 — Circle Question with Solution

JEE Main 2017 (08 Apr Online)

Question

If two parallel chords of a circle, having diameter 4 units, lie on the opposite sides of the center and subtend angles cos-1⁡17 and sec-1⁡7 at the center respectively, then the distance between these chords is:

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Show full solutionCorrect option: A
Correct answer
A87

Step-by-step explanation

Given condition, 

∴ cos⁡2θ=17 ⇒2cos2θ-1=17

⇒2cos2⁡θ=87

⇒cosθ=27

Then, CP1=rcosθ=47

Since, cos−117=sec−17, hence both the chords are at equal distance from center of the circle.

Hence, the distance between the chords =2 × 4 7 = 8 7 .

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About this question

This is a previous-year question from JEE Main 2017, covering the Circle chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.