Multiple choice

In a circle of radius 25 cm, a chord is drawn at a distance of 7 cm from the centre. Find the length of the chord

  1. 24 cm

  2. 48 cm

  3. 50 cm

  4. 36 cm
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B Correct answer
Explanation

In a circle, a perpendicular from the center to a chord bisects the chord. This forms a right triangle with the radius (25) as hypotenuse and the distance (7) as one leg. The half-chord length is sqrt(25^2 - 7^2) = sqrt(625 - 49) = sqrt(576) = 24. The full chord is 24 * 2 = 48 cm.

AI explanation

By the property that the perpendicular from the centre bisects the chord, we use the Pythagorean theorem with the radius of 25 cm and the distance of 7 cm. The half-length of the chord squared is 25 squared minus 7 squared, which is 625 minus 49, or 576. The half-length is the square root of 576, which is 24 cm. Therefore, the total length of the chord is 2 times 24 cm, giving 48 cm.

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