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Source:
December 31, 2021
geometry
Problem Statement
Hexagon
A
B
C
D
E
F
ABCDEF
A
BC
D
EF
has an inscribed circle
Ω
\Omega
Ω
that is tangent to each of its sides. If
A
B
=
12
AB = 12
A
B
=
12
,
∠
F
A
B
=
12
0
o
\angle FAB = 120^o
∠
F
A
B
=
12
0
o
, and
∠
A
B
C
=
15
0
o
\angle ABC = 150^o
∠
A
BC
=
15
0
o
, and if the radius of
Ω
\Omega
Ω
can be written as
m
+
n
m +\sqrt{n}
m
+
n
for positive integers
m
,
n
m, n
m
,
n
, find
m
+
n
m + n
m
+
n
.
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