Multiple choice

Find the radius of a circle, if a chord of length $8$ m is at a distance of $3$ m from the centre of the circle.

  1. $1$ m
  2. $2$ m
  3. $4$ m
  4. $5$ m
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D Correct answer
Explanation

A perpendicular from the center to a chord bisects the chord. This forms a right triangle with the radius as the hypotenuse, half the chord (4 m) as one leg, and the distance from the center (3 m) as the other leg. By the Pythagorean theorem, r = sqrt(4^2 + 3^2) = sqrt(16 + 9) = 5 m.

AI explanation

The perpendicular from the center to the chord bisects it, forming a right triangle with a leg of 4 m (half of the 8 m chord) and another leg of 3 m (the distance from the center). Using the Pythagorean theorem, the radius is the square root of (4^2 + 3^2). This equals the square root of 25, which is 5 m.

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