Multiple choice

A chord of length $30$ cm is drawn at a distance of $8$ cm from the centre of a circle. The radius of the circle (in cm.) is

  1. $15$ cm
  2. $21$ cm
  3. $18$ cm
  4. $17$ cm
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D Correct answer
Explanation

A perpendicular from the center to a chord bisects the chord. This forms a right-angled triangle with the distance from the center (8 cm) as one leg, half the chord (15 cm) as the other leg, and the radius as the hypotenuse. Using the Pythagorean theorem, r^2 = 8^2 + 15^2 = 64 + 225 = 289, so r = 17 cm.

AI explanation

The perpendicular from the center to a chord bisects the chord, creating a right triangle where the radius is the hypotenuse, half the chord is one leg, and the distance from the center is the other leg. Half of the 30 cm chord is 15 cm, and the distance from the center is 8 cm. Using the Pythagorean theorem, the radius is sqrt(15^2 + 8^2) = sqrt(225 + 64) = sqrt(289) = 17 cm.

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