MathDB

Around the outside of a

4

4

square, construct four semicircles (as shown in the figure) with the four sides of the square as their diameters. Another square,

ABCD

, has its sides parallel to the corresponding sides of the original square, and each side of

ABCD

is tangent to one of the semicircles. The area of the square

ABCD

is
[asy] pair A,B,C,D; A = origin; B = (4,0); C = (4,4); D = (0,4); draw(A--B--C--D--cycle); draw(arc((2,1),(1,1),(3,1),CCW)--arc((3,2),(3,1),(3,3),CCW)--arc((2,3),(3,3),(1,3),CCW)--arc((1,2),(1,3),(1,1),CCW)); draw((1,1)--(3,1)--(3,3)--(1,3)--cycle); dot(A); dot(B); dot(C); dot(D); dot((1,1)); dot((3,1)); dot((1,3)); dot((3,3)); label("

A

",A,SW); label("

B

",B,SE); label("

C

",C,NE); label("

D

",D,NW); [/asy]

\text{(A)}\ 16 \qquad \text{(B)}\ 32 \qquad \text{(C)}\ 36 \qquad \text{(D)}\ 48 \qquad \text{(E)}\ 64

Problem Statement