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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1055
GPA: 3.39
Trapezoid ABCD is inscribed in a circle. Parallel sides AB and CD are
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01 Apr 2021, 06:00
01 Apr 2021, 06:00
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Trapezoid ABCD is inscribed in a circle. Parallel sides AB and CD are 7 inches apart and 6 and 8 inches long, respectively. What is the radius of the circle in inches?
(A) 4
(B) 5
(C) \(4\sqrt{2}\)
(D) \(5\sqrt{2}\)
(E) 7
Trapezoid ABCD is inscribed in a circle. Parallel sides AB and CD are
[#permalink]
02 Apr 2021, 02:06
02 Apr 2021, 02:06
I cannot think of an exact solution. However, I can make a logical guess.
With the given measures of the trapezoid, we can find the area of the trapezoid.
Area of trapezoid \(= 1/2 * 7 * (8 + 6)\) = 49
Looking at the figure, I see that the trapezoid covers about 70% of the area of circle. Therefore, using the radii given in the answer choices, we can compare the area of trapezoid with the area of circle, and choose the best answer.
If r = 4, area of circle = 16 * pi ≃ 48 (taking pi = 3), almost same as the area of trapezoid. Eliminate.
If r = 5, area of circle = 25 * pi ≃ 75. Hold.
If r \(= 4\sqrt{2}\), area of circle = 32 * pi ≃ 96, nearly double the area of trapezoid. Eliminate.
B is my best guess.
With the given measures of the trapezoid, we can find the area of the trapezoid.
Area of trapezoid \(= 1/2 * 7 * (8 + 6)\) = 49
Looking at the figure, I see that the trapezoid covers about 70% of the area of circle. Therefore, using the radii given in the answer choices, we can compare the area of trapezoid with the area of circle, and choose the best answer.
If r = 4, area of circle = 16 * pi ≃ 48 (taking pi = 3), almost same as the area of trapezoid. Eliminate.
If r = 5, area of circle = 25 * pi ≃ 75. Hold.
If r \(= 4\sqrt{2}\), area of circle = 32 * pi ≃ 96, nearly double the area of trapezoid. Eliminate.
B is my best guess.
gmatclubot
Trapezoid ABCD is inscribed in a circle. Parallel sides AB and CD are [#permalink]
02 Apr 2021, 02:06
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