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Rectangle \(ABCD\) has length \(8\) and width \(6.\) What is the area of the circle?

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by VJesus12 » Thu Jul 30, 2020 8:58 am

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2019-04-30_1244.png
Rectangle \(ABCD\) has length \(8\) and width \(6.\) What is the area of the circle?

A. \(10\pi\)
B. \(25\pi\)
C. \(50\pi\)
D. \(64\pi\)
E. \(100\pi\)

[spoiler]OA=B[/spoiler]

Source: Princeton Review
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Re: Rectangle \(ABCD\) has length \(8\) and width \(6.\) What is the area of the circle?

by Scott@TargetTestPrep » Wed Aug 05, 2020 10:02 am
VJesus12 wrote: ↑
Thu Jul 30, 2020 8:58 am
 2019-04-30_1244.png

Rectangle \(ABCD\) has length \(8\) and width \(6.\) What is the area of the circle?

A. \(10\pi\)
B. \(25\pi\)
C. \(50\pi\)
D. \(64\pi\)
E. \(100\pi\)

[spoiler]OA=B[/spoiler]

Solution:

If a rectangle is inscribed in a circle, then its diagonal is the diameter of the circle. If we draw a diagonal of rectangle ABCD, say AC, we see that two 6-8-10 right triangles will be formed. Therefore, AC, which is also the diameter of the circle, is 10. So the radius of the circle is 5, and its area is 5^2 x π = 25π.

Answer: B

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