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National and Regional Contests
Poland Contests
Poland - Second Round
2017 Poland - Second Round
4
4
Part of
2017 Poland - Second Round
Problems
(1)
Geometry
Source: Polish MO
2/25/2017
Incircle of a triangle
A
B
C
ABC
A
BC
touches
A
B
AB
A
B
and
A
C
AC
A
C
at
D
D
D
and
E
E
E
, respectively. Point
J
J
J
is the excenter of
A
A
A
. Points
M
M
M
and
N
N
N
are midpoints of
J
D
JD
J
D
and
J
E
JE
J
E
. Lines
B
M
BM
BM
and
C
N
CN
CN
cross at point
P
P
P
. Prove that
P
P
P
lies on the circumcircle of
A
B
C
ABC
A
BC
.
geometry
circumcircle