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Saint Petersburg Mathematical Olympiad
2001 Saint Petersburg Mathematical Olympiad
10.3
10.3
Part of
2001 Saint Petersburg Mathematical Olympiad
Problems
(1)
AB+BC=3AC
Source: St. Petersburg MO 2001, 10th grade, P3
4/24/2023
Let
I
I
I
be the incenter of triangle
A
B
C
ABC
A
BC
and let
D
D
D
be the midpoint of side
A
B
AB
A
B
. Prove that if the angle
∠
A
O
D
\angle AOD
∠
A
O
D
is right, then
A
B
+
B
C
=
3
A
C
AB+BC=3AC
A
B
+
BC
=
3
A
C
.[I]Proposed by S. Ivanov
geometry
incenter