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National and Regional Contests
Paraguay Contests
Paraguay Mathematical Olympiad
2008 Paraguay Mathematical Olympiad
3
3
Part of
2008 Paraguay Mathematical Olympiad
Problems
(1)
Paraguayan National Olympiad 2008, Level 3, Problem 3
Source:
8/31/2014
Let
A
B
C
ABC
A
BC
be a triangle, where
A
B
=
A
C
AB = AC
A
B
=
A
C
and
B
C
=
12
BC = 12
BC
=
12
. Let
D
D
D
be the midpoint of
B
C
BC
BC
. Let
E
E
E
be a point in
A
C
AC
A
C
such that
D
E
⊥
A
C
DE \perp AC
D
E
⊥
A
C
. Let
F
F
F
be a point in
A
B
AB
A
B
such that
E
F
∥
B
C
EF \parallel BC
EF
∥
BC
. If
E
C
=
4
EC = 4
EC
=
4
, determine the length of
E
F
EF
EF
.
Asymptote