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The lengths of two sides in a right-angle triangle other than hypotenuse are 6 cm and 8 cm. If this right-angle...

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by BTGmoderatorLU » Wed Aug 05, 2020 3:56 am
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The lengths of two sides in a right-angle triangle other than hypotenuse are 6 cm and 8 cm. If this right-angle triangle is inscribed in a circle, then what is the are of the circle?

A. \(5\pi\)
B. \(10\pi\)
C. \(15\pi\)
D. \(20\pi\)
E. \(25\pi\)

The OA is E
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Re: The lengths of two sides in a right-angle triangle other than hypotenuse are 6 cm and 8 cm. If this right-angle...

by Scott@TargetTestPrep » Mon Aug 10, 2020 3:21 am
BTGmoderatorLU wrote: ↑
Wed Aug 05, 2020 3:56 am
 Source: e-GMAT

The lengths of two sides in a right-angle triangle other than hypotenuse are 6 cm and 8 cm. If this right-angle triangle is inscribed in a circle, then what is the are of the circle?

A. \(5\pi\)
B. \(10\pi\)
C. \(15\pi\)
D. \(20\pi\)
E. \(25\pi\)

The OA is E
Solution:

Since the legs of the right triangle are 6 cm and 8 cm, its hypotenuse must be 10 cm. When such a triangle is inscribed in a circle, its hypotenuse is also the diameter of the circle. Therefore, the diameter of the circle is 10 cm, and the radius is 5 cm. Since the radius is 5 cm, the area of the circle is π x 5^2 = 25π cm^2.

Answer: E

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