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Nordic
1994 Nordic
3
3
Part of
1994 Nordic
Problems
(1)
folding a square, perimeter question
Source: Nordic Mathematical Contest 1994 #3
10/4/2017
A piece of paper is the square
A
B
C
D
ABCD
A
BC
D
. We fold it by placing the vertex
D
D
D
on the point
D
′
D'
D
′
of the side
B
C
BC
BC
. We assume that
A
D
AD
A
D
moves on the segment
A
′
D
′
A' D'
A
′
D
′
and that
A
′
D
′
A' D'
A
′
D
′
intersects
A
B
AB
A
B
at
E
E
E
. Prove that the perimeter of the triangle
E
B
D
′
EBD'
EB
D
′
is one half of the perimeter of the square.
geometry