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Problem 3
2020 CVM - Problem 3
2020 CVM - Problem 3
Source: CVM 2020
July 16, 2020
geometry
Problem Statement
In
△
A
B
C
\triangle ABC
△
A
BC
we consider the points
A
′
,
B
′
,
C
′
A',B',C'
A
′
,
B
′
,
C
′
in sides
B
C
,
A
C
,
A
B
BC,AC,AB
BC
,
A
C
,
A
B
such that
3
B
A
′
=
C
A
′
,
3
C
B
′
=
A
B
′
,
3
A
C
′
=
B
A
′
3BA'=CA',~3CB'=AB',~3AC'=BA'
3
B
A
′
=
C
A
′
,
3
C
B
′
=
A
B
′
,
3
A
C
′
=
B
A
′
△
D
E
F
\triangle DEF
△
D
EF
is defined by the intersections of
A
A
′
,
B
B
′
,
C
C
′
AA',BB',CC'
A
A
′
,
B
B
′
,
C
C
′
. If the are of
△
A
B
C
\triangle ABC
△
A
BC
is
2020
2020
2020
find the area of
△
D
E
F
\triangle DEF
△
D
EF
.Proposed by Alejandro Madrid, Valle
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