The radius of circle O is 42, and OC = 15. The diagram is not drawn to scale. What is the length of segment AB? Round the answer to the nearest tenth. (1 point)

Question

Answer Choices:
78.5
39.2
29.2
58.5

Answer 1

To find the length of segment AB, we need to first find the length of chord AC using the formula:

AC = 2 * √(r^2 - OC^2)

Where r is the radius of the circle, which is 42 in this case. Plugging in the values:

AC = 2 * √(42^2 - 15^2)
AC = 2 * √(1764 - 225)
AC = 2 * √1539
AC ≈ 2 * 39.2
AC ≈ 78.5

Now, since segment AB is a diameter of the circle, it is equal to the sum of AC and BC. Therefore:

AB = AC + BC
AB = 78.5 + 42
AB = 120.5

Rounded to the nearest tenth, the length of segment AB is 120.5. Therefore, the closest answer choice is 78.5.

So, the answer is 78.5.