Bunuel wrote:

What is the area of the largest circle that can be inscribed in a semicircular region of radius r?

(A) πr^2/4

(B) πr^2/3

(C) πr^2/2

(D) 2πr^2/3

(E) 3πr^2/4

The largest circle that can be inscribed in a semicircular region of radius r is one with diameter = radius of the semicircle. In other words, the inscribed circle has a radius that is half of the radius of the circumscribed semicircle. Since the radius of the semicircle = r, the radius of the circle = r/2 and the area of the circle is:

π(r/2)^2 = π(r^2/4)

Answer: A

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Jeffery Miller

Head of GMAT Instruction

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