The distance of a chord 8 cm from the centre of a circle of radius 5 cm is
- $4\ cm$
- $3\ cm$
- $2\ cm$
- $9\ cm$
Reveal answer
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Correct answer
Explanation
A chord of length 8 cm is bisected by the perpendicular from the center, creating a right triangle with the radius (5 cm) as the hypotenuse and half the chord (4 cm) as one leg. The distance from the center is the other leg, calculated as sqrt(5^2 - 4^2) = sqrt(25 - 16) = sqrt(9) = 3 cm.
AI explanation
The perpendicular from the center of a circle to a chord bisects the chord, creating a right triangle with the radius as the hypotenuse. Here, the hypotenuse is the radius of 5 cm, and half the chord length is 4 cm. Using the Pythagorean theorem, the distance from the center is sqrt(5^2 - 4^2) = sqrt(25 - 16). This simplifies to sqrt(9), which gives a distance of 3 cm.