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Turkey Junior National Olympiad
1998 Turkey Junior National Olympiad
1
1
Part of
1998 Turkey Junior National Olympiad
Problems
(1)
Turkey Junior Olympiad 1998, Part II - P1
Source:
1/18/2013
Let
F
F
F
,
D
D
D
, and
E
E
E
be points on the sides
[
A
B
]
[AB]
[
A
B
]
,
[
B
C
]
[BC]
[
BC
]
, and
[
C
A
]
[CA]
[
C
A
]
of
△
A
B
C
\triangle ABC
△
A
BC
, respectively, such that
△
D
E
F
\triangle DEF
△
D
EF
is an isosceles right triangle with hypotenuse
[
E
F
]
[EF]
[
EF
]
. The altitude of
△
A
B
C
\triangle ABC
△
A
BC
passing through
A
A
A
is
10
10
10
cm. If
∣
B
C
∣
=
30
|BC|=30
∣
BC
∣
=
30
cm, and
E
F
∥
B
C
EF \parallel BC
EF
∥
BC
, calculate the perimeter of
△
D
E
F
\triangle DEF
△
D
EF
.
geometry
perimeter