Multiple choice

In a circle of radius $25$ cm two parallel chords of the length $14$ cm and $48$ cm respectively, are drawn on the same side of the centre. The distance between them is

  1. $14$ cm
  2. $24$ cm
  3. $17$ cm
  4. $31$ cm
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C Correct answer
Explanation

For a circle of radius 25, the distance from the center to a chord of length L is sqrt(R^2 - (L/2)^2). For L=14, d1 = sqrt(25^2 - 7^2) = sqrt(625 - 49) = 24. For L=48, d2 = sqrt(25^2 - 24^2) = sqrt(625 - 576) = 7. Since they are on the same side, the distance between them is 24 - 7 = 17 cm.

AI explanation

For the first chord of length 14 cm, half the chord is 7 cm, and using the Pythagorean theorem with the radius of 25 cm, the distance from the center is sqrt(25^2 - 7^2) = sqrt(625 - 49) = 24 cm. For the second chord of length 48 cm, half the chord is 24 cm, making its distance from the center sqrt(25^2 - 24^2) = sqrt(625 - 576) = 7 cm. Since both chords are on the same side of the center, the distance between them is the difference of their distances from the center, which is 24 - 7 = 17 cm.

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