Multiple choice

The distance between the two parallel chords of length 8 cm and 6 cm in a circle of diameter 10 cm if the chords lic on the same side of the centre is

  1. 1 cm

  2. 2 cm

  3. 3 cm

  4. 4 cm
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A Correct answer
Explanation

Radius = 5 cm. Distance of chord of length 8 from center = sqrt(5^2 - 4^2) = 3 cm. Distance of chord of length 6 from center = sqrt(5^2 - 3^2) = 4 cm. Since they are on the same side, the distance between them is 4 - 3 = 1 cm.

AI explanation

The distance from the center to a chord is found using the Pythagorean theorem, where the radius is the hypotenuse. For the 8 cm chord, the distance from the center is the square root of (5 squared minus 4 squared), which is 3 cm. For the 6 cm chord, the distance is the square root of (5 squared minus 3 squared), which is 4 cm. Because the chords are on the same side of the center, the distance between them is 4 minus 3, giving 1 cm.

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