Explanation:

Correct option 2: 6 cm

We are given:

• A circle with center O

• A chord AB = 24 cm, bisected by OD at point C, so AC = CB = 12 cm

• OD is perpendicular to chord AB (since it bisects it)

• Radius of the circle = 15 cm

• Point D lies on the circle

We are to find the length of CD, where C lies on AB and OD is perpendicular to AB.

Step-by-step solution:

Since OD ? AB and bisects it at C, we can use right triangle OCA:

• OC = ? (we'll find it)

• OA = radius = 15 cm

• AC = 12 cm

From triangle OAC:

OC²+AC²=OA² 

OC²+12²=15² 

OC²+ 144 =  225

OC²  =  225 - 144 = 81

OC= 9 cm

Now, since OD is perpendicular to AB, and C is the foot of perpendicular, then triangle ODC is a straight line.

So:

CD=OD−OC=15−9=6 cm