Bunuel wrote:

In the figure above, each arc is a semicircle. If AB = BD, and BC = CD, what is the ratio length of arc AD / length of arc CD?

(A) 4π/3

(B) 3π/2

(C) 3/1

(D) 4/1

(E) 9/2

Attachment:

2017-11-29_0805.png

We can let BC = CD = 1; thus AB = BD = 2. Therefore:

arc AD = 1/2 x (2 x π x 2) = 2π

and

arc CD = 1/2 x (2 x π x 1/2) = π/2

Thus, arc AD / arc CD = 2π/(π/2) = 2/(1/2) = 4/1.

Answer: D

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