Multiple choice

A chord of length $8\ cm$ is drawn at a distance of $3\ cm$ from the centre of a circle. Calculate the radius of the circle.

  1. $3$cm
  2. $5$cm
  3. $6$cm
  4. $8$cm
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B Correct answer
Explanation

A perpendicular from the center to a chord bisects the chord. This creates a right triangle with legs of 3 cm and 4 cm (half of 8 cm), where the hypotenuse is the radius. Using the Pythagorean theorem, sqrt(3^2 + 4^2) = 5 cm.

AI explanation

The perpendicular drawn from the centre of a circle to a chord bisects the chord, creating a right triangle with the radius as the hypotenuse. Here, the half-length of the chord is 4 cm (which is 8 cm divided by 2) and the perpendicular distance from the centre is 3 cm. Using the Pythagorean theorem, the radius is calculated as the square root of (4 squared plus 3 squared), which equals the square root of 25. Thus, the radius of the circle is 5 cm.

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