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2021 USMCA
25
2021 USMCA National Championship #25
2021 USMCA National Championship #25
Source:
May 9, 2021
Problem Statement
Convex equiangular hexagon
A
B
C
D
E
F
ABCDEF
A
BC
D
EF
has
A
B
=
C
D
=
E
F
=
3
AB = CD = EF = \sqrt 3
A
B
=
C
D
=
EF
=
3
and
B
C
=
D
E
=
F
A
=
2.
BC = DE = FA = 2.
BC
=
D
E
=
F
A
=
2.
Points
X
,
Y
,
X, Y,
X
,
Y
,
and
Z
Z
Z
are situated outside the hexagon such that
A
E
X
,
E
C
Y
,
AEX, ECY,
A
EX
,
EC
Y
,
and
C
A
Z
CAZ
C
A
Z
are all equilateral triangles. Compute the area of the region bounded by lines
X
F
,
Y
D
,
XF, YD,
XF
,
Y
D
,
and
Z
B
.
ZB.
ZB
.
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