Multiple choice

Two chords of length (a) unit and (b) unit of a circle make angles (60^\circ) and (90^\circ) at the centre of a circle respectively, then the correct relation is:

  1. $\(b = \sqrt{2}a\)$
  2. $\(b = 2a\)$
  3. $\(b = \sqrt{3}a\)$
  4. $\(b = \frac{3}{2}a\)$
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A Correct answer
Explanation

For a circle, chord length = 2r sin(θ/2) where θ is the angle at the center. For chord a: a = 2r sin(30°) = r. For chord b: b = 2r sin(45°) = √2r. Therefore b = √2a. This formula relates chord length to the central angle.

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