What Is a Circumscribed Circle?
In the above image, circle B is the triangle's circumscribed circle, and circle A is inscribed in the triangle. _O_ is the center of circle B. The radius of circle A is 4, and the radius of circle B is 9.
Which of the following values could be the area of the triangle?
Incorrect.
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The area of circle A is $$\pi (4)^2 = 16 \pi $$. Since $$\pi$$ is just above 3, $$16\pi$$ is more than 48. Therefore, you can __POE__ the answer choice of 42.
Incorrect.
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The area of circle A is $$\pi (4)^2 = 16 \pi $$. Since $$\pi$$ is just above 3, $$16\pi$$ is more than 48. Therefore, you can __POE__ the answer choice of 48.
Correct.
Since circle A is within the triangle and the triangle is within circle B, the area of the triangle must be between the areas of the two circles.
The area of circle A is $$\pi (4)^2 = 16 \pi $$. Since $$\pi$$ is just above 3, $$16\pi$$ is more than 48. Therefore, you can __POE__ the answer choices of 42 and 48.
The area of circle B is $$ \pi (9)^2 = 81 \pi $$. Since $$\pi$$ is just above 3, $$81\pi$$ is a bit more than 243. However, 275 is too large to be the value of $$81\pi$$. Therefore, you can __POE__ the answer choices of 275 and 299.
Since every other answer choice has been eliminated, 93 is the only possible value of the area of the triangle.
Incorrect.
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The area of circle B is $$ \pi (9)^2 = 81 \pi $$. Since $$\pi$$ is just above 3, $$81\pi$$ is a bit more than 243. However, 275 is too large to be the value of $$81\pi$$. Therefore, you can __POE__ the answer choice of 275.
Incorrect.
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The area of circle B is $$ \pi (9)^2 = 81 \pi $$. Since $$\pi$$ is just above 3, $$81\pi$$ is a bit more than 243. However, 299 is too large to be the value of $$25\pi$$. Therefore, you can __POE__ the answer choice of 299.
42
48
93
275
299
