Multiple choice

Choose the correct answer from the alternatives given. In a circle of radius $17$ cm two parallel chords are present on the opposite side of the diameter. If the distance between them is $23$ cm and the length of one chord is $16$ cm then the length of other chord is:

  1. $15$ cm
  2. $20$ cm
  3. $18$ cm
  4. $30$ cm
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the chords be AB and CD. Distance from center to chord AB (length 16) is sqrt(17^2 - 8^2) = sqrt(289 - 64) = 15. Since the chords are on opposite sides, the distance to the other chord is 23 - 15 = 8. The half-length of the other chord is sqrt(17^2 - 8^2) = sqrt(289 - 64) = 15. The full length is 15 * 2 = 30 cm.

AI explanation

Use the formula for chord length, which is twice the square root of the radius squared minus the distance squared. The radius is 17 cm, and the first chord is 16 cm, so its perpendicular distance from the center is the square root of 17 squared minus 8 squared, which is 15 cm. Since the chords are on opposite sides of the center and the total distance between them is 23 cm, the distance of the second chord from the center is 23 minus 15, equaling 8 cm. Calculate the length of the second chord as twice the square root of 17 squared minus 8 squared, which simplifies to twice 15, giving a length of 30 cm.

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