MathDB
Problems
Contests
International Contests
Nordic
1994 Nordic
1
1
Part of
1994 Nordic
Problems
(1)
inequality with cevians in equilateral
Source: Nordic Mathematical Contest 1994 #1
10/4/2017
Let
O
O
O
be an interior point in the equilateral triangle
A
B
C
ABC
A
BC
, of side length
a
a
a
. The lines
A
O
,
B
O
AO, BO
A
O
,
BO
, and
C
O
CO
CO
intersect the sides of the triangle in the points
A
1
,
B
1
A_1, B_1
A
1
,
B
1
, and
C
1
C_1
C
1
. Show that
O
A
1
+
O
B
1
+
O
C
1
<
a
OA_1 + OB_1 + OC_1 < a
O
A
1
+
O
B
1
+
O
C
1
<
a
.
inequalities
Equilateral Triangle