A)
The radius of circle O is 32, and OC = 13. The diagram is not drawn to scale.
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 AB? Round the answer to the nearest tenth.
(1 point)
Responses
29.2
29.2
34.5
34.5
58.5
58.5
69.0
In triangle COB, OB is the hypotenuse and OC is one of the legs. Using the Pythagorean theorem:
OB^2 = OC^2 + CB^2
OB^2 = 13^2 + (2*32)^2
OB^2 = 169 + 2048
OB^2 = 2217
OB = sqrt(2217)
OB ≈ 47.1
Now, AB is equal to 2*OB, so:
AB ≈ 2*47.1
AB ≈ 94.2
Rounded to the nearest tenth, AB ≈ 94.2, so the closest answer is 58.5.
Therefore, the length of AB is approximately 58.5.