Multiple choice

Radius of circle in which a chord of length $\sqrt {2}$ makes an angle $\cfrac { \pi }{ 2 } $ at the centre, is

  1. $1$
  2. $\sqrt {3}$
  3. $\cfrac { \sqrt { 3 } }{ 2 } $

  4. None of these
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A Correct answer
Explanation

For a chord of length L subtending angle theta at center, L = 2*r*sin(theta/2). sqrt(2) = 2*r*sin(pi/4) = 2*r*(1/sqrt(2)) = r*sqrt(2). So r = 1.

AI explanation

The two radii connecting to the ends of the chord form a right angle of pi/2 radians, creating an isosceles right triangle with the chord. In this triangle, the two equal sides are the radii of the circle, and the hypotenuse is the chord of length square root 2. Using the Pythagorean theorem, r squared plus r squared equals the square root of 2 squared, resulting in the equation 2r^2 = 2. Solving this gives a radius of 1.

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