Multiple choice

Directions: Compare the quantities and mark your answers as: In a circle of radius 5 cm, there are two parallel chords of lengths 6 cm and 4 cm, respectively. Quantity A Quantity B The distance between the chords 8.58 cm

  1. If quantity A is greater

  2. If quantity B is greater

  3. If both quantities are equal

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

The distance between parallel chords depends on whether they are on the same side or opposite sides of the center. With radius 5, the distances from the center are sqrt(5^2 - 3^2) = 4 and sqrt(5^2 - 2^2) = sqrt(21) approx 4.58. The distance between chords is either 4.58 - 4 = 0.58 or 4.58 + 4 = 8.58. Since both are possible, the relationship cannot be determined.

AI explanation

The perpendicular distance from the center to the 6 cm chord is found using the Pythagorean theorem: the square root of (5 squared minus 3 squared) equals 4 cm. The perpendicular distance to the 4 cm chord is the square root of (5 squared minus 2 squared), which is the square root of 21, approximately 4.58 cm. If the chords lie on opposite sides of the center, the distance between them is 4 plus 4.58, totaling 8.58 cm. If they lie on the same side, the distance is 4.58 minus 4, giving 0.58 cm. Because two different distances are possible, the relationship cannot be determined from the information given.

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