Multiple choice

14 cm long chord of a circle is at a distance of 24 cm from the centre. Find the radius of the circle.

  1. 5 cm

  2. 17 cm

  3. 25 cm

  4. 30 cm

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The perpendicular from the center to a chord bisects the chord. This forms a right triangle with the radius as the hypotenuse, half the chord (7 cm) as one leg, and the distance from the center (24 cm) as the other leg. Radius = sqrt(7^2 + 24^2) = sqrt(49 + 576) = sqrt(625) = 25.

AI explanation

Using the property of chords, the perpendicular from the center bisects the chord, giving a half-chord length of 7 cm. A right triangle is formed by the radius, the perpendicular distance of 24 cm, and the half-chord. By the Pythagorean theorem, the radius is the square root of (24^2 + 7^2) = the square root of (576 + 49) = the square root of 625, which is 25 cm.

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