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KoMaL A Problems
KoMaL A Problems 2019/2020
A. 771
A. 771
Part of
KoMaL A Problems 2019/2020
Problems
(1)
Nice Configuration
Source: KöMaL A. 771
3/20/2022
Let
ω
\omega
ω
denote the incircle of triangle
A
B
C
,
ABC,
A
BC
,
which is tangent to side
B
C
BC
BC
at point
D
.
D.
D
.
Let
G
G
G
denote the second intersection of line
A
D
AD
A
D
and circle
ω
.
\omega.
ω
.
The tangent to
ω
\omega
ω
at point
G
G
G
intersects sides
A
B
AB
A
B
and
A
C
AC
A
C
at points
E
E
E
and
F
F
F
respectively. The circumscribed circle of
D
E
F
DEF
D
EF
intersects
ω
\omega
ω
at points
D
D
D
and
M
.
M.
M
.
The circumscribed circle of
B
C
G
BCG
BCG
intersects
ω
\omega
ω
at points
G
G
G
and
N
.
N.
N
.
Prove that lines
A
D
AD
A
D
and
M
N
MN
MN
are parallel.Proposed by Ágoston Győrffy, Remeteszőlős
geometry
komal