Multiple choice

In a circle whose radius is $10$ inches, a chord is $6$ inches from the center. What is the length of the chord?

  1. $4$ inches
  2. $6$ inches
  3. $8$ inches
  4. $16$ inches
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D Correct answer
Explanation

The perpendicular from the center of a circle to a chord bisects the chord, forming a right triangle where the hypotenuse is the radius (10 inches) and one leg is the distance from the center (6 inches). Using the Pythagorean theorem, the other leg (half the chord length) is sqrt(10^2 - 6^2) = 8 inches, making the total chord length 16 inches.

AI explanation

Draw a perpendicular from the center to the chord, which bisects the chord and creates a right triangle with the radius as the hypotenuse. Using the Pythagorean theorem, half of the chord length is the square root of 10 squared minus 6 squared, which equals the square root of 64 or 8 inches. Multiplying this half-length by 2 gives the full chord length of 16 inches.

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