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.
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
1 answer