Multiple choice

The radius of a circle is 40 cm and the length of perpendicular drawn from its centre to chord is 24 cm. The length of chord is

  1. 32cm

  2. 64cm

  3. 8cm

  4. 16cm
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B Correct answer
Explanation

Radius = 40, distance to chord = 24. Half-chord = sqrt(40^2 - 24^2) = sqrt(1600 - 576) = sqrt(1024) = 32. Chord = 2 * 32 = 64.

AI explanation

By the property of circles, the perpendicular drawn from the center to a chord bisects the chord into two equal halves. We use the Pythagorean theorem on the right triangle formed by the radius, the perpendicular distance, and half the chord, giving half the chord squared as 40 squared minus 24 squared. This equals 1600 minus 576, which is 1024, so half the chord is 32 cm and the full length of the chord is 64 cm.

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