Multiple choice

If a chord of length $2\sqrt { 2 }$ subtends a right angle at the centre of the circle, then its radius is

  1. $\sqrt { 2 }$
  2. $2$
  3. $4$
  4. $1/2$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A chord of length L subtending angle theta at the center has L = 2r*sin(theta/2). Here L = 2*sqrt(2) and theta = 90 degrees. 2*sqrt(2) = 2r*sin(45) = 2r*(1/sqrt(2)) = r*sqrt(2). Thus r = 2.

AI explanation

Let the radius be r. Using the Pythagorean theorem for the right-angled triangle formed by the two radii and the chord, we write r squared plus r squared equals the square of the chord length. This gives 2r squared equals the square of 2 times the square root of 2, which is 8. Solving r squared equals 4 yields a radius of 2.

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