Multiple choice

In a circle of radius 5 cm PQ and RS are two prajallel chords of length 8 cm & 6 cm respectively lying onthe opposite sides of sides of center The distance between the chords is

  1. 1 cm

  2. 5 cm

  3. 6 cm

  4. 7 cm
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D Correct answer
Explanation

The distances of the chords from the center are sqrt(5^2 - 4^2) = 3 cm and sqrt(5^2 - 3^2) = 4 cm. Since the chords lie on opposite sides of the center, the distance between them is 3 + 4 = 7 cm.

AI explanation

A line from the center perpendicular to a chord bisects it, creating right triangles to find the distance from the center to each chord. For chord PQ of length 8 cm, the distance from the center is found by the Pythagorean theorem as the square root of (5^2 minus (8/2)^2), which is 3 cm. For chord RS of length 6 cm, the distance is the square root of (5^2 minus (6/2)^2), giving 4 cm. Since the chords lie on opposite sides of the center, the total distance between them is the sum of these distances, 3 cm plus 4 cm, which equals 7 cm.

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