Multiple choice

The radius of a circle with centre $P$ is $25$ cm and the length of the chord is $48$ cm. The distance of the chord from centre $P$ of the circle is

  1. $24$ cm
  2. $5$ cm
  3. $7$ cm
  4. $12$ cm
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C Correct answer
Explanation

The distance from the center to the chord bisects the chord. Using Pythagoras: r^2 = d^2 + (chord/2)^2 => 25^2 = d^2 + 24^2 => 625 = d^2 + 576 => d^2 = 49 => d = 7.

AI explanation

Draw a perpendicular from centre P to the chord, which bisects the 48 cm chord into two segments of 24 cm each. Using the Pythagoras theorem in the right-angled triangle formed by the radius, the half-chord, and the perpendicular distance, we calculate the distance as the square root of 25 squared minus 24 squared. This equals the square root of 625 minus 576, which is the square root of 49. The distance of the chord from the centre is 7 cm.

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