Multiple choice

Two parallel chords of a circle with diameter $13\ cm$ are, $5\ cm$ and $12\ cm$ in length. If both the chords lies in a semi-circle, find the distance between the chords

  1. $8.5\ cm$
  2. $5\ cm$
  3. $3.5\ cm$
  4. $3\ cm$
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C Correct answer
Explanation

The radius of the circle is 6.5 cm. The distance of the 5 cm chord from the center is sqrt(6.5^2 - 2.5^2) = 6 cm. The distance of the 12 cm chord from the center is sqrt(6.5^2 - 6^2) = 2.5 cm. Since they are on the same side of the center, the distance between them is 6 - 2.5 = 3.5 cm.

AI explanation

The circle has a radius of 6.5 cm, and the perpendicular from the center bisects each chord into lengths of 2.5 cm and 6 cm. Using the Pythagorean theorem, the distances from the center to the chords are the square root of 6.5 squared minus 2.5 squared, which is 6 cm, and the square root of 6.5 squared minus 6 squared, which is 2.5 cm. Because both chords lie in the same semicircle, we subtract the smaller distance from the larger one to get 3.5 cm.

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