Multiple choice

A chord of length 12 cm is drawn in a circle of diameter 20 cm. The distance of the chord from the centre is

  1. 8 cm

  2. 6 cm

  3. 10 cm

  4. 16 cm
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A Correct answer
Explanation

The radius of the circle is 10 cm. A perpendicular from the center to a 12 cm chord bisects it into two 6 cm segments. This forms a right triangle with hypotenuse 10 and base 6. The distance is sqrt(10^2 - 6^2) = sqrt(100 - 36) = sqrt(64) = 8 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. The diameter is 20 cm, so the radius is 10 cm, and half of the 12 cm chord is 6 cm. Using the Pythagorean theorem, the distance d from the center squared plus the half-chord squared equals the radius squared. Calculating this gives d^2 + 6^2 = 10^2, so d^2 = 100 - 36 = 64, and d = 8 cm.

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