The radius of a circle is 15 cm and the length of one of its chords is 24 cm. Find the distance of the chord from the centre.

Let AB be a chord of a circle with centre O and radius 15 cm such that AB = 24 cm.

We draw OL ⊥ AB and join OA.

Since the perpendicular from the centre of a circle to a chord bisects the chord.

∴ AL = LB = AB/2 = 12 cm

Now in △OAL, we have

OA² = OL² + AL²      [By Pythagoras theorem]

⇒ OL² = OA² - AL²

⇒ OL² = (15)² - (12)²

⇒ OL² = 225 - 144 = 81

⇒ OL = 9 cm

Hence the distance of the chord from the centre is 9 cm.