Multiple choice

$O$ is the centre of the circle having radius $5$ cm. $OM$ is a $\perp$ on chord $AB$. If $OM = 4$ cm, then the length of the chord $AB$ is equal to

  1. $5$ cm
  2. $6$ cm
  3. $8$ cm
  4. $10$ cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In triangle OMA, OA is the radius (5), OM is the perpendicular distance (4). By Pythagoras, AM^2 = 5^2 - 4^2 = 25 - 16 = 9, so AM = 3. The chord AB = 2 * AM = 6.

AI explanation

By the property of circles, a perpendicular drawn from the center to a chord bisects the chord, creating a right triangle with the radius as the hypotenuse. Using the Pythagorean theorem, half the length of chord AB is the square root of (5 squared minus 4 squared), which is the square root of 9, or 3 cm. Since the perpendicular OM bisects AB, the full length of the chord is twice this distance. Multiplying 3 cm by 2 gives the length of chord AB as 6 cm.

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