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Problems
Contests
National and Regional Contests
Bulgaria Contests
Bulgarian Winter Tournament
2024 Bulgarian Winter Tournament
9.3
9.3
Part of
2024 Bulgarian Winter Tournament
Problems
(1)
Well-known conditional geo
Source: Bulgarian Winter Tournament 2024 9.3
1/28/2024
Let
A
B
C
ABC
A
BC
be a triangle, satisfying
2
A
C
=
A
B
+
B
C
2AC=AB+BC
2
A
C
=
A
B
+
BC
. If
O
O
O
and
I
I
I
are its circumcenter and incenter, show that
∠
O
I
B
=
9
0
∘
\angle OIB=90^{\circ}
∠
O
I
B
=
9
0
∘
.
geometry