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Czech-Polish-Slovak Match
2021 Czech-Austrian-Polish-Slovak Match
2
2
Part of
2021 Czech-Austrian-Polish-Slovak Match
Problems
(1)
Classic configuration revisited
Source: 2021 Czech-Polish-Slovak Match, P2
8/3/2021
In an acute triangle
A
B
C
ABC
A
BC
, the incircle
ω
\omega
ω
touches
B
C
BC
BC
at
D
D
D
. Let
I
a
I_a
I
a
be the excenter of
A
B
C
ABC
A
BC
opposite to
A
A
A
, and let
M
M
M
be the midpoint of
D
I
a
DI_a
D
I
a
. Prove that the circumcircle of triangle
B
M
C
BMC
BMC
is tangent to
ω
\omega
ω
.Patrik Bak (Slovakia)
geometry
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