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International Contests
Baltic Way
2023 Baltic Way
11
11
Part of
2023 Baltic Way
Problems
(1)
Config with reflection of the excenter
Source: Baltic Way 2023/11
11/11/2023
Let
A
B
C
ABC
A
BC
be triangle with
A
A
A
-excenter
J
J
J
. The reflection of
J
J
J
in
B
C
BC
BC
is
K
K
K
. The points
E
E
E
and
F
F
F
are on
B
J
,
C
J
BJ, CJ
B
J
,
C
J
such that
∠
E
A
B
=
∠
C
A
F
=
9
0
∘
\angle EAB=\angle CAF=90^{\circ}
∠
E
A
B
=
∠
C
A
F
=
9
0
∘
. Prove that
∠
F
K
E
+
∠
F
J
E
=
18
0
∘
\angle FKE+\angle FJE=180^{\circ}
∠
F
K
E
+
∠
F
J
E
=
18
0
∘
.
geometry