Multiple choice

A chord of length 60 cm is at a distance of 16 cm from the centre of a circle. What is the radius (in cm) of the circle?

  1. 17

  2. 34

  3. 51

  4. 68
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A perpendicular from the center to a chord bisects the chord. This creates a right triangle with the radius as the hypotenuse, half the chord (30 cm) as one leg, and the distance from the center (16 cm) as the other leg. Radius = sqrt(30^2 + 16^2) = sqrt(900 + 256) = sqrt(1156) = 34.

AI explanation

A line from the centre of a circle perpendicular to a chord bisects the chord, forming a right triangle with the radius. Half of the chord length is 30 cm, and the distance from the centre is 16 cm. Using the Pythagorean theorem, the radius is the square root of (30^2 + 16^2). This equals the square root of (900 + 256), which is the square root of 1156, making the radius 34 cm.

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