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Serbia JBMO TST
2024 Serbia JBMO TST
4
4
Part of
2024 Serbia JBMO TST
Problems
(1)
Geometry about a well-known lemma
Source: Serbia JBMO TST 2024 P4
5/25/2024
Let
I
I
I
be the incenter of a triangle
A
B
C
ABC
A
BC
with
A
B
≠
A
C
AB \neq AC
A
B
=
A
C
. Let
M
M
M
be the midpoint of
B
C
BC
BC
,
M
′
∈
B
C
M' \in BC
M
′
∈
BC
be such that
I
M
′
=
I
M
IM'=IM
I
M
′
=
I
M
and
K
K
K
be the midpoint of the arc
B
A
C
BAC
B
A
C
. If
A
K
∩
B
C
=
L
AK \cap BC=L
A
K
∩
BC
=
L
, show that
K
L
I
M
′
KLIM'
K
L
I
M
′
is cyclic.
geometry