Multiple choice

The radius of a circle with centre $O$ is $41$. The length of the chord $PQ$ of same circle is $80$. The distance of chord $PQ$ from centre $O$ is

  1. $81$ cm
  2. $27$ cm
  3. $3$ cm
  4. $9$ cm
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D Correct answer
Explanation

In a circle, the perpendicular from the center to a chord bisects the chord. This forms a right triangle with hypotenuse = radius (41), base = half-chord (40), and height = distance (d). d^2 + 40^2 = 41^2. d^2 + 1600 = 1681. d^2 = 81, d = 9.

AI explanation

The perpendicular drawn from the center of a circle to a chord bisects the chord, creating a right triangle with the radius as the hypotenuse. Half of the chord PQ is 80 / 2 = 40. Using the Pythagorean theorem, the distance from the center is sqrt(41^2 - 40^2) = sqrt(1681 - 1600) = sqrt(81) = 9. The distance of the chord from the center is 9.

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