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Problems
Contests
National and Regional Contests
China Contests
(China) National High School Mathematics League
2000 China Second Round Olympiad
1
1
Part of
2000 China Second Round Olympiad
Problems
(1)
A problem about equal areas
Source: 2000 China Second Round Olympiad P1
8/13/2019
In acute-angled triangle
A
B
C
,
ABC,
A
BC
,
E
,
F
E,F
E
,
F
are on the side
B
C
,
BC,
BC
,
such that
∠
B
A
E
=
∠
C
A
F
,
\angle BAE=\angle CAF,
∠
B
A
E
=
∠
C
A
F
,
and let
M
,
N
M,N
M
,
N
be the projections of
F
F
F
onto
A
B
,
A
C
,
AB,AC,
A
B
,
A
C
,
respectively. The line
A
E
AE
A
E
intersects
⊙
(
A
B
C
)
\odot (ABC)
⊙
(
A
BC
)
at
D
D
D
(different from point
A
A
A
). Prove that
S
A
M
D
N
=
S
△
A
B
C
.
S_{AMDN}=S_{\triangle ABC}.
S
A
M
D
N
=
S
△
A
BC
.
geometry