Multiple choice

The length of a chord which is at a distance of 6 cm from the centre of a circle of radius 10 cm is

  1. 18cm

  2. 20cm

  3. 12cm

  4. 16cm
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D Correct answer
Explanation

Using Pythagoras theorem, half-chord = sqrt(10^2 - 6^2) = sqrt(100 - 36) = 8. Full chord = 16 cm.

AI explanation

The perpendicular drawn from the center of a circle to a chord bisects the chord, creating a right triangle with the radius as the hypotenuse. Using the Pythagorean theorem, half the chord length is sqrt(10^2 - 6^2) = sqrt(64) = 8 cm. Multiplying this by 2 gives the full length of the chord as 16 cm.

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