Multiple choice

The diameter of a circle is $7$ cm. Which one of the chords are closest to the center?

  1. $AB=2$ cm
  2. $BC=3$ cm
  3. $EF=3$ cm
  4. $GH=6$ cm
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D Correct answer
Explanation

The distance of a chord from the center is inversely proportional to its length. The longest chord is the diameter (7 cm). The chord closest to the center is the one with the greatest length. GH = 6 cm is the longest chord listed.

AI explanation

Using the perpendicular distance formula, the distance from the center to a chord equals the square root of the radius squared minus half the chord length squared. The radius is half the diameter of 7 cm, which is 3.5 cm, and the corresponding squared distances for the given options are 10.5, 8.5, 8.5 and 0.5. Since GH equals 6 cm produces the smallest distance of 0.5 cm, it is the chord closest to the center.

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