Multiple choice

The length of chord of circle with radius $5cm$ and the chord at a distance of $3cm$ from the center is

  1. $8cm$
  2. $10cm$
  3. $12cm$

  4. None
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A Correct answer
Explanation

A perpendicular from the center to a chord bisects the chord. Using the Pythagorean theorem on the triangle formed by the radius, the distance to the chord, and half the chord length: r^2 = d^2 + (L/2)^2. 5^2 = 3^2 + (L/2)^2. 25 = 9 + (L/2)^2. 16 = (L/2)^2. L/2 = 4. L = 8.

AI explanation

Using the property that the perpendicular from the center bisects the chord, we apply the Pythagorean theorem to the right triangle formed by the radius, the distance to the chord, and half the chord length. The formula is half chord length equals the square root of (radius squared minus distance squared), which is $\sqrt{5^2 - 3^2} = \sqrt{16} = 4$ cm. The full length is twice this value, so the chord is 8 cm.

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