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Ecuador Contests
Ecuador Mathematical Olympiad (OMEC)
2020 Ecuador NMO (OMEC)
5
5
Part of
2020 Ecuador NMO (OMEC)
Problems
(1)
Proving inequality geometry problem
Source: OMEC Ecuador National Olympiad Final Round 2020 N3 P5 day 2
11/11/2024
In triangle
A
B
C
ABC
A
BC
,
D
D
D
is the middle point of side
B
C
BC
BC
and
M
M
M
is a point on segment
A
D
AD
A
D
such that
A
M
=
3
M
D
AM=3MD
A
M
=
3
M
D
. The barycenter of
A
B
C
ABC
A
BC
and
M
M
M
are on the inscribed circumference of
A
B
C
ABC
A
BC
. Prove that
A
B
+
A
C
>
3
B
C
AB+AC>3BC
A
B
+
A
C
>
3
BC
.
geometry
inequalities
circumcircle