Multiple choice

In a circle of radius 17 cm, a chord is at a distance of 15 cm from the centre of the circle. What is the length of the chord?

  1. 15 cm

  2. 12 cm

  3. 8 cm

  4. 16 cm
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D Correct answer
Explanation

A chord, the radius, and the distance from the center form a right triangle where the radius is the hypotenuse. Using the Pythagorean theorem: (half-chord)^2 + 15^2 = 17^2. (half-chord)^2 = 289 - 225 = 64. Half-chord = 8, so the full chord length is 16 cm.

AI explanation

The perpendicular from the center to the chord bisects it, creating a right triangle with the radius as the hypotenuse. Using the Pythagorean theorem, half the chord length is the square root of (17 squared minus 15 squared), which equals the square root of (289 minus 225), or 8 cm. The full length of the chord is 2 multiplied by 8 cm, resulting in 16 cm.

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