Final answer:
To calculate the length of CD, you can use the approximation that the length of the chord AB is approximately equal to the length of the corresponding arc. Using this approximation and the given values, the length of CD is 12cm.
Step-by-step explanation:
To calculate the length of CD, we can use the approximation that the length of the chord AB is approximately equal to the length of the corresponding arc. In this case, the arc length is equal to the circumference of the circle times the angle formed by AB. Since the radius of the circle is 18cm, the circumference is 2πr = 2(3.1415927...)(18cm) ≈ 113.097cm. The angle formed by AB can be calculated using the formula: angle = length of AB / circumference = 12cm / 113.097cm.
Using the angle, we can now find the length of CD by calculating the arc length formed by the angle on the larger circle. The arc length can be calculated using the formula: arc length = circumference × angle = 113.097cm × (12cm / 113.097cm) = 12cm.