Multiple choice

The distance of a chord AB of a circle from the centre is 8cm less than the radius, , If the radius of the circle is less than the length of the chord by 11cm then the respective lengths of the chord, the radius and the distance of chord from the centre are

  1. 13cm, 24cm, 5cm, and 29cm, 40cm, 21cm.

  2. 24cm, 13cm, 5cm, and 40cm, 29cm, 21cm.

  3. 24cm, 5cm, 13cm, and 40cm, 21cm, 29cm.

  4. 5cm, 13cm, 24cm, and 21cm, 29cm, 40cm.
Reveal answer Fill a bubble to check yourself
B Correct answer
AI explanation

Let the radius be r, the chord be c, and the distance from the center be d. We have d = r - 8 and r = c - 11. Using the property of intersecting chords where a perpendicular from the center bisects the chord, r squared equals d squared plus (c/2) squared. Solving the equations yields two valid sets of dimensions: a 24 cm chord, 13 cm radius, 5 cm distance, and a 40 cm chord, 29 cm radius, 21 cm distance.

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