Multiple choice

A chord of length 16 cm is a distance of 15 cm from the centre of the circle. Then the length of the chord of the same circle which is at a distance of 8 cm from the centre is

  1. 64cm

  2. 60cm

  3. 32cm

  4. 30 cm
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D Correct answer
Explanation

Radius squared = (chord/2)^2 + distance^2. R^2 = 8^2 + 15^2 = 64 + 225 = 289. R = 17. For the second chord, (chord/2)^2 + 8^2 = 17^2. (chord/2)^2 = 289 - 64 = 225. chord/2 = 15. Chord = 30.

AI explanation

Using the perpendicular from the centre to a chord bisects the chord property, the half-length is 8 cm, so applying the Pythagorean theorem gives a radius squared of 15 squared plus 8 squared, or 289. For a chord 8 cm from the centre, the half-length squared is 289 minus 8 squared, which is 225, making the half-length 15 cm. The full length of this chord is 2 times 15 cm, which is 30 cm.

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