Multiple choice

A chord of length 10 cm is at a distance of 12 cm from the centre of the circle. The radius of the circle is

  1. 13 cm

  2. 13.5 cm

  3. 12 cm

  4. 15.6 cm
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A Correct answer
Explanation

The perpendicular from the center to the chord bisects it. This forms a right triangle with the radius as the hypotenuse, half-chord (5 cm) as one leg, and distance (12 cm) as the other. Radius = sqrt(5^2 + 12^2) = sqrt(25 + 144) = 13.

AI explanation

The perpendicular from the center of a circle to a chord bisects the chord, creating a right triangle with the radius as the hypotenuse. The legs of this right triangle are half the chord length, which is 10 / 2 = 5 cm, and the distance from the center, which is 12 cm. Applying the Pythagorean theorem, the radius r = sqrt(5^2 + 12^2) = sqrt(25 + 144) = sqrt(169) = 13 cm.

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