Multiple choice

In a circle with radius 8 centimeters, there are two parallel chords. The first chord is positioned 3 centimeters away from the center of the circle, and the second chord is positioned 5 centimeters away from the center. Quantity A: Distance between the chords Quantity B: 6.93 centimeters

  1. Quantity A is greater.

  2. Quantity B is greater.

  3. The two quantities are equal.

  4. The relationship cannot be determined from the information given.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Distance from center to chord 1 is d1=3, chord 2 is d2=5. Half-length of chord 1 is sqrt(8^2 - 3^2) = sqrt(55) approx 7.41. Half-length of chord 2 is sqrt(8^2 - 5^2) = sqrt(39) approx 6.24. The distance between chords depends on whether they are on the same or opposite sides of the center. If same side, distance = 5-3 = 2. If opposite, distance = 5+3 = 8. Neither is 6.93.

AI explanation

Because the chords are parallel, they can either be on opposite sides of the center or the same side. If they are on opposite sides, the distance between them is 8 centimeters, making Quantity A greater. If they are on the same side, the distance is 2 centimeters, making Quantity B greater. Since the exact positions are not specified, a definite relationship cannot be established.

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