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International Contests
APMO
2020 APMO
1
1
Part of
2020 APMO
Problems
(1)
AC, BF, DE concurrent
Source: APMO 2020 Problem 1
6/9/2020
Let
Γ
\Gamma
Γ
be the circumcircle of
△
A
B
C
\triangle ABC
△
A
BC
. Let
D
D
D
be a point on the side
B
C
BC
BC
. The tangent to
Γ
\Gamma
Γ
at
A
A
A
intersects the parallel line to
B
A
BA
B
A
through
D
D
D
at point
E
E
E
. The segment
C
E
CE
CE
intersects
Γ
\Gamma
Γ
again at
F
F
F
. Suppose
B
B
B
,
D
D
D
,
F
F
F
,
E
E
E
are concyclic. Prove that
A
C
AC
A
C
,
B
F
BF
BF
,
D
E
DE
D
E
are concurrent.
geometry
concurrency