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).

9 6 4 10

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