MathDB
Problems
Contests
National and Regional Contests
Greece Contests
Greece Junior Math Olympiad
2014 Greece Junior Math Olympiad
1
1
Part of
2014 Greece Junior Math Olympiad
Problems
(1)
triangle ABC, # BCDE, BE//AM, BE=AM/2, midpoint (Greece Junior 2014)
Source:
7/14/2019
Let
A
B
C
ABC
A
BC
be a triangle and let
M
M
M
be the midpoint
B
C
BC
BC
. On the exterior of the triangle, consider the parallelogram
B
C
D
E
BCDE
BC
D
E
such that
B
E
/
/
A
M
BE//AM
BE
//
A
M
and
B
E
=
A
M
/
2
BE=AM/2
BE
=
A
M
/2
. Prove that line
E
M
EM
EM
passes through the midpoint of segment
A
D
AD
A
D
.
geometry
parallelogram
midpoint