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APMO
2008 APMO
3
3
Part of
2008 APMO
Problems
(1)
Two lines meet at circle
Source: APMO 2008 problem 3
3/22/2008
Let
Γ
\Gamma
Γ
be the circumcircle of a triangle
A
B
C
ABC
A
BC
. A circle passing through points
A
A
A
and
C
C
C
meets the sides
B
C
BC
BC
and
B
A
BA
B
A
at
D
D
D
and
E
E
E
, respectively. The lines
A
D
AD
A
D
and
C
E
CE
CE
meet
Γ
\Gamma
Γ
again at
G
G
G
and
H
H
H
, respectively. The tangent lines of
Γ
\Gamma
Γ
at
A
A
A
and
C
C
C
meet the line
D
E
DE
D
E
at
L
L
L
and
M
M
M
, respectively. Prove that the lines
L
H
LH
L
H
and
M
G
MG
MG
meet at
Γ
\Gamma
Γ
.
geometry
circumcircle
APMO