MathDB
Problems
Contests
International Contests
IMO Longlists
1992 IMO Longlists
5
5
Part of
1992 IMO Longlists
Problems
(1)
AI || OH iff BAC = 120 degrees
Source:
9/1/2010
Let
I
,
H
,
O
I,H,O
I
,
H
,
O
be the incenter, centroid, and circumcenter of the nonisosceles triangle
A
B
C
ABC
A
BC
. Prove that
A
I
∥
H
O
AI \parallel HO
A
I
∥
H
O
if and only if
∠
B
A
C
=
12
0
∘
\angle BAC =120^{\circ}
∠
B
A
C
=
12
0
∘
.
geometry
incenter
circumcircle
Centroid
IMO Shortlist
IMO Longlist