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MBMT Guts Rounds
2015.22
2015.22
Part of
MBMT Guts Rounds
Problems
(1)
MBMT Guts #22
Source:
3/29/2015
In rhombus ABCD,
∠
A
=
6
0
∘
\angle A = 60^\circ
∠
A
=
6
0
∘
. Rhombus
B
E
F
G
BEFG
BEFG
is constructed, where
E
E
E
and
G
G
G
are the midpoints of
B
C
BC
BC
and
A
B
AB
A
B
, respectively. Rhombus
B
H
I
J
BHIJ
B
H
I
J
is constructed, where
H
H
H
and
J
J
J
are the midpoints of
B
E
BE
BE
and
B
G
BG
BG
, respectively. This process is repeated forever. If the area of
A
B
C
D
ABCD
A
BC
D
and the sum of the areas of all of the rhombi are both integers, compute the smallest possible value of
A
B
AB
A
B
.