MathDB
Problems
Contests
National and Regional Contests
Belarus Contests
Belarus Team Selection Test
2019 Belarus Team Selection Test
1.2
1.2
Part of
2019 Belarus Team Selection Test
Problems
(1)
Inequality with medians
Source: 2019 Belarus Team Selection Test 1.2
9/2/2019
Points
M
M
M
and
N
N
N
are the midpoints of the sides
B
C
BC
BC
and
A
D
AD
A
D
, respectively, of a convex quadrilateral
A
B
C
D
ABCD
A
BC
D
. Is it possible that
A
B
+
C
D
>
max
(
A
M
+
D
M
,
B
N
+
C
N
)
?
AB+CD>\max(AM+DM,BN+CN)?
A
B
+
C
D
>
max
(
A
M
+
D
M
,
BN
+
CN
)?
(Folklore)
inequalities
geometry