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).
Answer & explanation
Correct answer: option 2
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