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Re: Triangle ABC is inscribed in a semicircle. What is the area of the sh [#permalink]
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Bunuel wrote:

Triangle ABC is inscribed in a semicircle. What is the area of the shaded region above?

(A) \(2\pi-2\)

(B) \(2\pi - 4\)

(C) \(4\pi - 4\)

(D) \(8\pi - 4\)

(E) \(8\pi - 8\)

Attachment:
2018-02-14_0952.png


First of all, we should observe that the angle ABC is an angle subtended by a diameter, therefore it is a right angle.

We see that we have an isosceles right triangle (45-45-90) in which AC = hypotenuse of triangle = diameter of the semicircle. Recall that the ratio of a leg of a 45-45-90 triangle to its hypotenuse is x : x√2.

Thus, AC = 2√2 x √2 = 4, so we know the circle’s diameter is 4 and its radius is 2.

The area of the semicircle is 1/2 x π x 2^2 = 2π.

The area of the triangle is (1/2)*(2√2)^2 = 8/2 = 4.

Thus, the area of the shaded region is 2π - 4.

Answer: B
GMAT Club Bot
Re: Triangle ABC is inscribed in a semicircle. What is the area of the sh [#permalink]
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