11

Part of 2015 ASDAN Math Tournament

Problems(2)

Source:

In the following diagram, each circle has radius

6

and each circle passes through the center of the other two circles. Compute the area of the white center region and express your answer in terms of

\pi

.

Source:

ABCDEF

be a regular hexagon, and let

G

H

I

J

K

L

be the midpoints of sides

AB

BC

CD

DE

EF

FA

, respectively. The intersection of lines

\overline{AH}

\overline{BI}

\overline{CJ}

\overline{DK}

\overline{EL}

\overline{FG}

bound a smaller regular hexagon. Find the ratio of the area of the smaller hexagon to the area of

ABCDEF