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CHMMC problems
2019 CHMMC (Fall)
1
1
Part of
2019 CHMMC (Fall)
Problems
(1)
2019 Fall Team #1
Source:
4/17/2022
Let
A
B
C
ABC
A
BC
be an equilateral triangle of side length
6
6
6
. Points
D
,
E
D, E
D
,
E
and
F
F
F
are on sides
A
B
AB
A
B
,
B
C
BC
BC
, and
A
C
AC
A
C
respectively such that
A
D
=
B
E
=
C
F
=
2
AD = BE = CF = 2
A
D
=
BE
=
CF
=
2
. Let circle
O
O
O
be the circumcircle of
D
E
F
DEF
D
EF
, that is, the circle that passes through points
D
,
E
D, E
D
,
E
, and
F
F
F
. What is the area of the region inside triangle
A
B
C
ABC
A
BC
but outside circle
O
O
O
?
geometry