If two parallel chords of a circle, having diameter 4 units, lie on the opposite sides of the center and subtend angles cos^(-1)⁡1/7 and sec^(-1)⁡7 at…

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)⁡1/7 and sec^(-1)⁡7 at the center respectively, then the distance between these chords is:

MARKS Content Team · Accepted Answer

Correct answer: (A) 8/(√7). Given condition, ∴ cos⁡2θ=1/7 ⇒2cos^2θ-1=1/7 ⇒2cos^2⁡θ=8/7 ⇒cosθ=(2√7Then, CP_1=rcosθ=4√7Since, cos^(−1)1)/7=sec^(−1)7, hence both the chords are at equal distance from center of the circle. Hence, the distance between the chords =2 × 4/(√7) =8/(√7) .

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

Solution

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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:

Solution

Relevant Questions

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