The radius of circle O is 32, and OC = 13.
A circle is shown with a center O, radius OB and chord ACB. Right triangle COB is shown inside of the circle.
What is the length of segment AB? Round your answer to the nearest tenth.
(1 point)
Responses
180
180
100
100
58.5
58.5
29.2
The length of segment AB can be found using the Pythagorean theorem.
Let x be the length of AB.
OB is the radius of the circle, which is 32.
In triangle COB, OB is the hypotenuse, OC is one leg, and x/2 is the other leg (since segment AB is a chord and hence its midpoint is equidistant from the center of the circle).
Using the Pythagorean theorem:
(OC)^2 + (x/2)^2 = (OB)^2
13^2 + (x/2)^2 = 32^2
169 + (x/2)^2 = 1024
(x/2)^2 = 1024 - 169
(x/2)^2 = 855
x/2 = √855
x = 2√855
Approximately, x is equal to 29.2.
Therefore, the length of segment AB is approximately 29.2.
Correct response: 29.2