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Benelux Olympiad 2020, Problem 3 (tangent circles through triangle vertices)
Source: BxMO 2020, Problem 3
5/2/2020
Let
A
B
C
ABC
A
BC
be a triangle. The circle
ω
A
\omega_A
ω
A
through
A
A
A
is tangent to line
B
C
BC
BC
at
B
B
B
. The circle
ω
C
\omega_C
ω
C
through
C
C
C
is tangent to line
A
B
AB
A
B
at
B
B
B
. Let
ω
A
\omega_A
ω
A
and
ω
C
\omega_C
ω
C
meet again at
D
D
D
. Let
M
M
M
be the midpoint of line segment
[
B
C
]
[BC]
[
BC
]
, and let
E
E
E
be the intersection of lines
M
D
MD
M
D
and
A
C
AC
A
C
. Show that
E
E
E
lies on
ω
A
\omega_A
ω
A
.
geometry
BxMO
Benelux