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National and Regional Contests
Greece Contests
Greece Junior Math Olympiad
1999 Greece Junior Math Olympiad
3
3
Part of
1999 Greece Junior Math Olympiad
Problems
(1)
AB=DB+BD_1, AC=CE+CE_1 in a equilateral (Greece Junior 1999)
Source:
7/12/2019
Let
A
B
C
ABC
A
BC
be an equilateral triangle . Let point
D
D
D
lie on side
A
B
,
E
AB,E
A
B
,
E
lie on side
A
C
,
D
1
AC, D_1
A
C
,
D
1
and
E
1
E_1
E
1
lie on side BC such that
A
B
=
D
B
+
B
D
1
AB=DB+BD_1
A
B
=
D
B
+
B
D
1
and
A
C
=
C
E
+
C
E
1
AC=CE+CE_1
A
C
=
CE
+
C
E
1
. Calculate the smallest angle between the lines
D
E
1
DE_1
D
E
1
and
E
D
1
ED_1
E
D
1
.
geometry
Equilateral