Bunuel wrote:

In the figure above, O is the center of the circle, and B is a point on the circle. In rectangle OABC, if OA = 4 and OC = 5, what is the area of the circle?

(A) 9π

(B) 16π

(C) 25π

(D) 41π

(E) 64π

Attachment:

2017-11-14_1157.png

Rectangle OABC's diagonal = hypotenuse of right triangle ABO = radius of the circle.

If OC = 5, AB = 5 = one leg

OA = 4 = other leg

The sum of the squares of the legs of a right triangle equal the hypotenuse squared, where the hypotenuse = the radius.

\(4^2 + 5^2 = r^2\)

\(16 + 25 = r^2\)

\(r = \sqrt{41}\)

Circle area =

\(\pi*r^2 = \pi*(\sqrt{41})^2 = 41\pi\)

Answer D

_________________

In the depths of winter, I finally learned

that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"