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Austrian-Polish
1979 Austrian-Polish Competition
1
1
Part of
1979 Austrian-Polish Competition
Problems
(1)
On sides AB and BC of a square ABCD respective points E and F
Source: 1979 Austrian-Polish Mathematical Competition p1
2/15/2020
On sides
A
B
AB
A
B
and
B
C
BC
BC
of a square
A
B
C
D
ABCD
A
BC
D
the respective points
E
E
E
and
F
F
F
have been chosen so that
B
E
=
B
F
BE = BF
BE
=
BF
. Let
B
N
BN
BN
be the altitude in triangle
B
C
E
BCE
BCE
. Prove that
∠
D
N
F
=
90
\angle DNF = 90
∠
D
NF
=
90
.
geometry
square
right angle
equal segments