Multiple choice

A chord of a circle of radius $10$ cm subtends a right angle at its centre. The length of the chord (in cm) is

  1. $\displaystyle 5\sqrt { 2 } $
  2. $\displaystyle 10\sqrt { 2 } $
  3. $\displaystyle \frac { 5 }{ \sqrt { 2 } } $
  4. $\displaystyle 10\sqrt { 3 } $
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B Correct answer
Explanation

A chord subtending a right angle at the center forms an isosceles right triangle with the two radii. Using the Pythagorean theorem, the chord length is sqrt(10^2 + 10^2) = sqrt(200) = 10*sqrt(2).

AI explanation

The chord and the two radii form a right-angled isosceles triangle at the center. Using the Pythagorean theorem, the chord length squared equals 10 squared plus 10 squared, which is 200. Taking the square root of 200 gives a chord length of 10 times the square root of 2.

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