Multiple choice

The length of chord of circle with radius 10cm drawn at a distance of 8cm

  1. 12cm

  2. 10cm

  3. 14cm

  4. 30cm
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A Correct answer
Explanation

A perpendicular from the center to the chord bisects the chord. This forms a right triangle with the radius (10 cm) as the hypotenuse and the distance (8 cm) as one leg. The half-chord length is sqrt(10^2 - 8^2) = sqrt(100 - 64) = sqrt(36) = 6 cm. The full chord length is 2 * 6 = 12 cm.

AI explanation

The perpendicular from the centre to the chord bisects it, forming a right triangle with the radius as the hypotenuse. Using the Pythagorean theorem, half the chord squared equals 10 squared minus 8 squared, giving 100 minus 36 equals 64. The square root of 64 is 8, so the full chord length is 2 times 8, which is 12 cm.

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