Multiple choice

$AB$ is chord of a circle with centre $O$ and radius $17$ cm. If $OM \perp AB$ and $OM = 8$ cm. The length of chord $AB$ is

  1. $12$ cm
  2. $30$ cm
  3. $15$ cm
  4. $24$ cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In triangle OMA, OA = 17 (radius), OM = 8. By Pythagoras, AM^2 = 17^2 - 8^2 = 289 - 64 = 225. AM = 15. Chord AB = 2 * AM = 30.

AI explanation

The perpendicular drawn from the center of a circle to a chord bisects the chord, meaning AM equals BM. Applying the Pythagorean theorem to the right triangle OMA gives AM squared as 17 squared minus 8 squared, which is 289 minus 64 to equal 225, so AM is 15 cm. The full length of the chord AB is twice the length of AM, resulting in 30 cm.

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