Multiple choice

The radius of a circle with centre O is $13$cm. The distance of a chord from the centre is $5$ cm.Find the length of the chord.

  1. $24$cm
  2. $12$cm
  3. $13$cm
  4. $26$cm
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A perpendicular from the center to a chord bisects the chord. This forms a right triangle with the radius (13) as the hypotenuse and the distance (5) as one leg. The other leg (half the chord) is sqrt(13^2 - 5^2) = sqrt(169 - 25) = sqrt(144) = 12. The total chord length is 12 * 2 = 24.

AI explanation

Draw a perpendicular from the center O to the chord, which bisects the chord and forms a right triangle with the radius. Using the Pythagorean theorem with the radius as the hypotenuse (13 cm) and the distance as one leg (5 cm), the half-length of the chord is sqrt(13^2 - 5^2) = sqrt(169 - 25) = 12 cm. The full length of the chord is twice this value, which is 24 cm. The correct option is A.

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