Bunuel wrote:

In the figure above, the vertices of rectangle ABCD lie on a circle with center O. If BD = 8, CD = 4 and x = 120, what is the perimeter of the shaded region?

(A) 8π/3 + 2√3

(B) 8π/3 + 4√2

(C) 8π/3 + 4√3

(D) 8π + 2√3

(E) 8π + 4√3

Attachment:

2017-11-22_1022_003.png

We see that the perimeter of the shaded region consists of side BC of the rectangle and arc BC of the circle. Let’s first determine the length of side BC of the rectangle.

Using the Pythagorean theorem, we have:

4^2 + b^2 = 8^2

16 + b^2 = 64

b^2 = 48

b = √48 = √16 x √3 = 4√3 = side BC

Since the diagonal BD = 8 = diameter of the circle, the circumference of the circle = 8π. Since arc BC corresponds to a central angle of 120 degrees, the length of arc BC = (120/360) x 8π = (1/3) x 8π = 8π/3.

Thus, the perimeter of the shaded region = 8π/3 + 4√3.

Answer: C

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Jeffery Miller

Head of GMAT Instruction

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