Bunuel wrote:

The figure above shows portions of two circles with centers at A and C respectively, and square ABCD with side of length s. What is the perimeter of the curved figure in terms of s?

(A) 4πs/3

(B) 3πs/2

(C) 2πs

(D) 3πs

(E) 4πs

Attachment:

2017-11-23_1215.png

Perimeter = \(\frac{3}{4}\) circumference of one circle * 2Vertex A of square ABCD = 90°. That 90° "cuts" (shortens) the perimeter of circle with center A by \(\frac{90}{360}=\frac{1}{4}\)

One part of the perimeter of the curved figure hence is \(\frac{3}{4}\) of the circumference of Circle A.

Vertex C of the square does exactly the same thing to the circle with center C.

So perimeter of curved figure =

\(\frac{3}{4}\) circumference of Circle A +

\(\frac{3}{4}\) circumference of Circle C

Radius of both circles = square's side length = \(s\)

Circumference of each circle:\(2πr = 2πs\)

Perimeter of curved figure:

\((2) * (\frac{3}{4} *2πs)=\frac{12πs}{4}=3πs\)

Answer D

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In the depths of winter, I finally learned

that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"