Bunuel wrote:

In the figure above, a square with side of length √2 is inscribed in a circle. If the area of the circle is kπ, what is the value of k?

(A) 1/2

(B) 3/4

(C) 1

(D) 2

(E) 2√2

Attachment:

2017-11-17_0947_001.png

Use the square's diagonal to find diameter and radius of circle. Calculate circle's area. Set calculated area of circle equal to kπ.

The diagonal of a square with side s*:

\(s\sqrt{2}\)Given:

\(s = \sqrt{2}\)Diagonal length hence = \(\sqrt{2}*\sqrt{2}=2\)

Square's diagonal length =

length of circle's diameter, d

d = 2, and d = 2r

2 = 2r, r = 1

Area of circle = \(πr^2= (π)(1) = 1π\)

The area of the circle also = kπ

kπ = 1π

k = 1

Answer C

**OR

\(side^2 + side^2 = diagonal^2\)

\((\sqrt{2})^2 + (\sqrt{2})^2 = d^2\)

\((2 + 2) = 4 = d^2\)

\(d = 2\)
_________________

In the depths of winter, I finally learned

that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"