Multiple choice

The length of a chord of a circle at a distance of 5 cm from the centre is 24 cm. the diameter of the circle is

  1. 26 cm

  2. 24 cm

  3. 13 cm

  4. 12 cm
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A Correct answer
Explanation

A perpendicular from the center to a chord bisects it. Half-chord = 12cm, distance = 5cm. Radius^2 = 12^2 + 5^2 = 144 + 25 = 169. Radius = 13cm. Diameter = 2 * 13 = 26cm.

AI explanation

The perpendicular from the center to a chord bisects the chord, forming a right triangle where the radius is the hypotenuse, the distance from the center is one leg, and half the chord length is the other leg. Using the Pythagorean theorem, r^2 = 5^2 + 12^2 = 25 + 144 = 169, so the radius r is 13 cm. The diameter is twice the radius, which is 2 times 13, yielding 26 cm.

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