Multiple choice

A circle with diameter 25 cm has a chord of length 21 cm. Find perpendicular distance of chord from the center.

  1. √23 cm

  2. √69 cm

  3. √46 cm

  4. √92 cm

  5. None of these
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C Correct answer
Explanation

The distance from the center to a chord is the leg of a right triangle where the hypotenuse is the radius (12.5 cm) and the other leg is half the chord length (10.5 cm). Using the Pythagorean theorem, d^2 = 12.5^2 - 10.5^2 = 156.25 - 110.25 = 46. Thus, the distance is sqrt(46) cm.

AI explanation

The perpendicular from the center of a circle to a chord bisects the chord, creating a right triangle where the radius is the hypotenuse. The radius of the circle is 25 divided by 2, which is 12.5 cm, and half the chord length is 21 divided by 2, which is 10.5 cm. Using the Pythagorean theorem, the perpendicular distance is the square root of (12.5 squared minus 10.5 squared). This simplifies to the square root of (156.25 minus 110.25), which equals the square root of 46 cm.

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