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Greece Junior Math Olympiad
2023 Greece Junior Math Olympiad
2
2
Part of
2023 Greece Junior Math Olympiad
Problems
(1)
BD=2 EN if CD // ME , AM=//MB, AN=//NC
Source: Greece Junior Math Olympiad 2023 p2
3/2/2024
In triangle
A
B
C
ABC
A
BC
, points
M
M
M
,
N
N
N
are the midpoints of sides
A
B
AB
A
B
,
A
C
AC
A
C
respelctively. Let
D
D
D
and
E
E
E
be two points on line segment
B
N
BN
BN
such that
C
D
∥
M
E
CD \parallel ME
C
D
∥
ME
and
B
D
<
B
E
BD <BE
B
D
<
BE
. Prove that
B
D
=
2
⋅
E
N
BD=2\cdot EN
B
D
=
2
⋅
EN
.
equal segments
geometry