JEE Main 2017 · 8 Apr · Shift 1 · Mathematics Q79

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MathematicsSingle correct+4 / -1Question 79 of 90

If two parallel chords of a circle, having diameter 4 units, lie on the opposite sides of the centre and subtend angles $\cos^{-1}\left(\dfrac17\right)$ and $\sec^{-1}(7)$ at the centre respectively, then the distance between these chords, is :

\dfrac4{\sqrt7}

\dfrac8{\sqrt7}

\dfrac87

\dfrac{16}7

Answer and worked solution

Official answer: B

A chord subtending θ is at distance $r\cos\frac\theta2$ from the centre. $\sec^{-1}7=\cos^{-1}\frac17$ , so both angles are equal, with $\cos\frac\theta2=\sqrt{\frac{1+1/7}2}=\frac2{\sqrt7}$ . Each chord is $\frac4{\sqrt7}$ from the centre, on opposite sides: $\frac8{\sqrt7}$ apart.

Topics:Equation of a circle Inverse trigonometric functions

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JEE Main 2017 · 8 Apr · Shift 1, Mathematics question 79