Multiple choice

Find the distance of the chord from the center. A chord of length $16$ m is drawn in a circle of diameter $20$ m.

  1. $3$ m
  2. $6$ m
  3. $9$ m
  4. $12$ m
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B Correct answer
Explanation

The radius of the circle is 10 m. A perpendicular from the center to the chord bisects the chord into two 8 m segments. Using the Pythagorean theorem, distance^2 + 8^2 = 10^2. distance^2 = 100 - 64 = 36. distance = 6 m.

AI explanation

The radius of the circle is half of the 20 m diameter, which is 10 m, and the perpendicular from the center bisects the 16 m chord into two 8 m segments. Using the Pythagorean theorem, the distance from the center is the square root of 10 squared minus 8 squared. This calculates to the square root of 36, making the distance 6 m.

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