Multiple choice

Determine the length of a chord, which is at a distance of $7$ cm from the center of the circle of radius $25$ cm.

  1. $25$ cm
  2. $48$ cm
  3. $16$ cm
  4. $24$ cm
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B Correct answer
Explanation

A perpendicular from the center to a chord bisects the chord. Using Pythagoras: (half-chord)^2 + 7^2 = 25^2. (half-chord)^2 = 625 - 49 = 576. Half-chord = 24. Full chord = 48 cm.

AI explanation

The perpendicular from the center to the chord bisects it, forming a right triangle with the radius as the hypotenuse. By the Pythagorean theorem, half the chord length is the square root of 25 squared minus 7 squared, which is the square root of 625 minus 49, or 24 cm. Multiplying this half-length by 2 gives the full length of the chord as 48 cm.

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