Multiple choice

The length of the chord of a circle is $8$cm and perpendicular distance between centre and the chord is $3$cm. Then the radius of the circle is equal to?

  1. 4 cm

  2. 5 cm

  3. 6 cm

  4. 8 cm
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B Correct answer
Explanation

A perpendicular from the center to a chord bisects the chord. This forms a right triangle with the radius as the hypotenuse, half the chord (4 cm) as one leg, and the distance to the chord (3 cm) as the other leg. By Pythagorean theorem, r^2 = 4^2 + 3^2 = 16 + 9 = 25, so r = 5.

AI explanation

The perpendicular from the centre to a chord bisects the chord, creating a right triangle with the radius. Using the Pythagorean theorem, the radius squared equals 3 squared plus 4 squared, giving 9 plus 16 equals 25. The radius is the square root of 25, which is 5 cm.

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