Question
Line AB intersects circle C at points A and B, as shown,
and is 5 cm long. If line AB is 2 cm from the center of
the circle C, what is the area of circle C to the nearest
tenth of a centimeter?
A.
3.2
B.
20.1
C.
25.6
D.
32.2
E.
78.6
and is 5 cm long. If line AB is 2 cm from the center of
the circle C, what is the area of circle C to the nearest
tenth of a centimeter?
A.
3.2
B.
20.1
C.
25.6
D.
32.2
E.
78.6
Answers
GPT 3.5
We can use the Pythagorean theorem to find the radius of circle C. Since AB is 2 cm from the center of the circle, we have a right triangle with legs of 2 cm and 5 cm.
Using the Pythagorean theorem, we get:
radius^2 + 2^2 = 5^2
radius^2 + 4 = 25
radius^2 = 21
radius = sqrt(21)
Now, we can calculate the area of circle C using the formula A = πr^2:
A = π(√21)^2
A = π(21)
A ≈ 66.1 cm^2
Therefore, the area of circle C is approximately 66.1 cm^2 to the nearest tenth of a centimeter.
The closest answer choice is not provided, so we must round it to the nearest answer choice, which is 78.6.
Therefore, the answer is E. 78.6.
Using the Pythagorean theorem, we get:
radius^2 + 2^2 = 5^2
radius^2 + 4 = 25
radius^2 = 21
radius = sqrt(21)
Now, we can calculate the area of circle C using the formula A = πr^2:
A = π(√21)^2
A = π(21)
A ≈ 66.1 cm^2
Therefore, the area of circle C is approximately 66.1 cm^2 to the nearest tenth of a centimeter.
The closest answer choice is not provided, so we must round it to the nearest answer choice, which is 78.6.
Therefore, the answer is E. 78.6.