A circle with centre O has radius 15 cm. D is a point on the circle such that a 24 cm long chord Ab is bisected by OD at point C. Find the length of CD (in cm).

6

We have,

OD = OA = 15 cm (radius)

AB = 24 cm

AC = CB = 12 cm

In right-angled triangle OAC,

AC² + OC² = OA²  

= OC² = 15² – 12² = 81

= OC = 9 cm

Now, CD = OD – OC

We know, OD = 15 cm

= CD = 15 – 9 = 6 cm