Multiple choice

If two parallel chords of length 8 cm and 6 cm in a circle of radius 5 cm are on the opposite sides of the center then the distance between the parallel chords is

  1. $5\ cm$
  2. $6\ cm$
  3. $7\ cm$

  4. None of these
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C Correct answer
Explanation

Distance from center to chord of length 8 is sqrt(5^2 - 4^2) = 3. Distance to chord of length 6 is sqrt(5^2 - 3^2) = 4. Since they are on opposite sides, the total distance is 3 + 4 = 7 cm.

AI explanation

Using the property that the perpendicular from the center to a chord bisects the chord, we find the distance to each chord from the center using the Pythagorean theorem. For the 8 cm chord, the distance is sqrt(5^2 - 4^2) = sqrt(25 - 16) = 3 cm. For the 6 cm chord, the distance is sqrt(5^2 - 3^2) = sqrt(25 - 9) = 4 cm. Since the chords are on opposite sides of the center, the total distance between them is the sum of these distances, which is 3 cm + 4 cm = 7 cm.

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