Multiple choice

In a circle of radius 17 cm, two parallel chords of lengths 30 cm and 16 cm are drawn. If both the chords are on the same side of the centre, then the distance between the chords is

  1. 9 cm

  2. 7 cm

  3. 23 cm

  4. 11 cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Distance from center to chord of length 30 is sqrt(17^2 - 15^2) = 8. Distance to chord of length 16 is sqrt(17^2 - 8^2) = 15. Since both are on the same side, the distance between them is 15 - 8 = 7 cm.

AI explanation

A perpendicular from the center to the 30 cm chord bisects it, creating a right triangle with a hypotenuse of 17 and a base of 15. Using the Pythagorean theorem, the distance from the center to this chord is the square root of (17 squared minus 15 squared), which equals 8. For the 16 cm chord, the base is 8, so its distance from the center is the square root of (17 squared minus 8 squared), which equals 15. Since both chords are on the same side of the center, the distance between them is 15 minus 8, which is 7 cm.

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