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Problems
Contests
National and Regional Contests
Netherlands Contests
Dutch Mathematical Olympiad
1969 Dutch Mathematical Olympiad
3
3
Part of
1969 Dutch Mathematical Olympiad
Problems
(1)
ED = EB if AB = BD = DC, AC = BC, AE = AB
Source: Netherlands - Dutch NMO 1969 p3
2/1/2023
Given a quadrilateral
A
B
C
D
ABCD
A
BC
D
with
A
B
=
B
D
=
D
C
AB = BD = DC
A
B
=
B
D
=
D
C
and
A
C
=
B
C
AC = BC
A
C
=
BC
. On
B
C
BC
BC
lies point
E
E
E
such that
A
E
=
A
B
AE = AB
A
E
=
A
B
. Prove that
E
D
=
E
B
ED = EB
E
D
=
EB
.
geometry
equal segments