Multiple choice

The chord of a circle is 20 cm away from the centre of the circle and is 1.2 times its radius. Find the length of the chord.

  1. 15 cm

  2. 20 cm

  3. 25 cm

  4. 30 cm

  5. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let r be radius. Chord length L = 1.2r. Distance d = 20. r^2 = d^2 + (L/2)^2. r^2 = 20^2 + (0.6r)^2. r^2 = 400 + 0.36r^2. 0.64r^2 = 400. r^2 = 400 / 0.64 = 625. r = 25. Chord length = 1.2 * 25 = 30.

AI explanation

Let the radius be r, which makes the chord length 1.2r. The line from the centre perpendicular to the chord bisects it, creating a right triangle with sides r, 20, and 0.6r. Using the Pythagorean theorem, we have r^2 = 20^2 + (0.6r)^2, which simplifies to r^2 = 400 + 0.36r^2. Solving for r^2 gives 0.64r^2 = 400, so r^2 = 625 and r = 25 cm. The chord length is 1.2 * 25, which equals 30 cm.

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