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Greece Junior Math Olympiad
2013 Greece Junior Math Olympiad
2
2
Part of
2013 Greece Junior Math Olympiad
Problems
(1)
equal segments lead to equal segments (Greece Junior 2013)
Source:
7/14/2019
Let
A
B
C
ABC
A
BC
be an acute angled triangle with
A
B
<
A
C
AB<AC
A
B
<
A
C
. Let
M
M
M
be the midpoint of side
B
C
BC
BC
. On side
A
B
AB
A
B
, consider a point
D
D
D
such that, if segment
C
D
CD
C
D
intersects median
A
M
AM
A
M
at point
E
E
E
, then
A
D
=
D
E
AD=DE
A
D
=
D
E
. Prove that
A
B
=
C
E
AB=CE
A
B
=
CE
.
geometry