Find the length of a chord which is at a distance of 9 cm from the centre of a circle of radius 15 cm.

Given radius(AO) = 15cm

Length of the chord (AB) = x

distance of the chord from the centre is 9cm.

Draw a perpendicular bisector from center to the chord and name it OC.

AC = BC

Now in ∆ AOC

Using Pythagoras theorem

AO² = AC² + OC²

15² = AC² + 9²

AC² = 15² – 9²

AC² = 225 – 81

AC² = 144

AC = 12cm

BC = 12cm

The length of the chord is AC + BC = 12 + 12 = 24 cm.