MathDB

Let circle

O

have radius

5

with diameter

\overline{AE}

. Point

F

is outside circle

O

such that lines

\overline{F A}

and

\overline{F E}

intersect circle

O

at points

B

and

D

, respectively. If

F A = 10

and

m \angle F AE = 30^o

, then the perimeter of quadrilateral ABDE can be expressed as

a + b\sqrt2 + c\sqrt3 + d\sqrt6

, where

a, b, c

, and

d

are rational. Find

a + b + c + d

2