Question

The radius of circle O is 32, and OC = 13. What is the length of segment AB? Round your answer to the nearest tenth. (1 point) Responses 29.2 29.2 180 180 100 100 58.5

Answer 1

To find the length of segment \( AB \), we can use the following approach:

1. Since \( O \) is the center of the circle and \( C \) is a point inside the circle, we can use the Pythagorean theorem. Let \( A \) and \( B \) be the points where the line perpendicular to \( OC \) intersects the circle.

2. The distance \( OA \) (or \( OB \)) is the radius of the circle, which is \( 32 \).

3. The distance \( OC \) is given as \( 13 \). Let \( D \) be the point where the perpendicular from \( C \) to \( AB \) meets \( AB \).

4. According to the Pythagorean theorem:
\[
OA^2 = OC^2 + CD^2
\]
Plugging in the values, we have:
\[
32^2 = 13^2 + CD^2
\]
\[
1024 = 169 + CD^2
\]
\[
CD^2 = 1024 - 169
\]
\[
CD^2 = 855
\]
\[
CD = \sqrt{855} \approx 29.2
\]

5. Since \( D \) is the midpoint of \( AB \), segment \( AB \) is twice the length of \( CD \):
\[
AB = 2 \times CD \approx 2 \times 29.2 = 58.4
\]

Rounding to the nearest tenth, the length of segment \( AB \) is approximately **58.5**.

So the correct answer is \( \boxed{58.5} \).