Multiple choice

The perpendicular from the centre of a circle to a chord is 16 cm in length. If the diameter of the circle is 40 cm, then what is the length of the chord?

  1. 12 cm

  2. 16 cm

  3. 24 cm

  4. 30 cm
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C Correct answer
Explanation

The radius of the circle is half the diameter, which is 20 cm. Using the Pythagorean theorem on the triangle formed by the radius, the perpendicular distance (16 cm), and half the chord length, we get sqrt(20^2 - 16^2) = sqrt(400 - 256) = sqrt(144) = 12 cm. The total chord length is twice this value, which is 24 cm.

AI explanation

The radius of the circle is half of the diameter, so r equals 40 divided by 2, which is 20 cm. The perpendicular from the centre to the chord bisects the chord, creating a right triangle where the hypotenuse is the radius (20 cm) and one leg is the perpendicular distance (16 cm). Using the Pythagorean theorem, half the chord length equals the square root of (20 squared minus 16 squared), which is the square root of (400 minus 144), or the square root of 256. This gives half the chord as 12 cm; multiplying by 2 gives the total chord length of 24 cm.

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