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Niels Henrik Abels Math Contest (Norwegian Math Olympiad) Final Round
2023 Abelkonkurransen Finale
1b
1b
Part of
2023 Abelkonkurransen Finale
Problems
(1)
The centroid of ABC lies on ME [2023 Abel, Problem 1b]
Source:
3/12/2024
In the triangle
A
B
C
ABC
A
BC
, points
D
D
D
and
E
E
E
lie on the side
B
C
BC
BC
, with
C
E
=
B
D
CE = BD
CE
=
B
D
. Also,
M
M
M
is the midpoint of
A
D
AD
A
D
. Show that the centroid of
A
B
C
ABC
A
BC
lies on
M
E
ME
ME
.
geometry