A chord of a circle is 30 cm long. Its distance from the centre is 8 cm. Find the radius of the circle.

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Solution

In the given circle, length of the chord is 30 cm. Distance of the chord, AB, from the centre is 8 cm.
Seg AM = seg MB = 15 cm (Perpendicular drawn from the centre to a chord bisects the chord)
By using Pythagoras theorem, in right triangle AOM,
AM² + OM² = OA²
⇒ 15² + 8² = OA²
⇒ 225 + 64 = OA²
⇒ OA² = 225 + 64
⇒ OA² = 289
⇒ OA = 17 cm
Therefore, the radius of the circle is 17 cm.

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