Multiple choice

What is the diameter of a circle, if a chord of length $24$ m is at a distance of $5$ m from the center of the circle?

  1. $13$ m
  2. $12$ m
  3. $26$ m
  4. $11$ m
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C Correct answer
Explanation

A perpendicular from the center to a chord bisects the chord. This forms a right triangle with the radius as the hypotenuse, half the chord (12m) as one leg, and the distance (5m) as the other. r^2 = 12^2 + 5^2 = 144 + 25 = 169. r = 13. Diameter = 2r = 26m.

AI explanation

The perpendicular from the center to the chord bisects it, creating a right triangle with legs of 12 m and 5 m. Using the Pythagorean theorem, the radius is the square root of (12^2 + 5^2), which equals 13 m. The diameter is twice the radius, so the diameter is 26 m.

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