Question

The radius of a circle is 17 cm. Find the length of a chord which is at a distance of 8 cm from the centre of the circle.

Answer 1

In the given circle, radius = OA = 17 cm and distance of the chord AB from the centre is 8 cm, i.e. OM = 8 cm .
So, Seg AM = Seg MB (Perpendicular drawn from the centre to a chord bisects the chord)



By using Pythagoras Theorem in triangle OAM, we get:
AM² + OM² = OA²
⇒ AM² = 289 − 64
⇒ AM² = 225
⇒ AM = 15 cm
But Seg AM = Seg MB
∴ Seg AB = Seg AM + Seg MB = 30 cm
So, the length of the chord is 30 cm.