MathDB
Problems
Contests
International Contests
Cono Sur Olympiad
2018 Cono Sur Olympiad
5
5
Part of
2018 Cono Sur Olympiad
Problems
(1)
Fifth problem
Source: Cono sur 2018
8/27/2018
Let
A
B
C
ABC
A
BC
be an acute-angled triangle with
∠
B
A
C
=
6
0
∘
\angle BAC = 60^{\circ}
∠
B
A
C
=
6
0
∘
and with incenter
I
I
I
and circumcenter
O
O
O
. Let
H
H
H
be the point diametrically opposite(antipode) to
O
O
O
in the circumcircle of
△
B
O
C
\triangle BOC
△
BOC
. Prove that
I
H
=
B
I
+
I
C
IH=BI+IC
I
H
=
B
I
+
I
C
.
geometry
incenter
circumcircle
cono sur