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National and Regional Contests
Argentina Contests
Argentina Cono Sur TST
2013 Argentina Cono Sur TST
5
5
Part of
2013 Argentina Cono Sur TST
Problems
(1)
Argentina Cono Sur TST 2013. Problem 5
Source:
1/3/2015
Let
A
B
C
ABC
A
BC
be an equilateral triangle and
D
D
D
a point on side
A
C
AC
A
C
. Let
E
E
E
be a point on
B
C
BC
BC
such that
D
E
⊥
B
C
DE \perp BC
D
E
⊥
BC
,
F
F
F
on
A
B
AB
A
B
such that
E
F
⊥
A
B
EF \perp AB
EF
⊥
A
B
, and
G
G
G
on
A
C
AC
A
C
such that
F
G
⊥
A
C
FG \perp AC
FG
⊥
A
C
. Lines
F
G
FG
FG
and
D
E
DE
D
E
intersect in
P
P
P
. If
M
M
M
is the midpoint of
B
C
BC
BC
, show that
B
P
BP
BP
bisects
A
M
AM
A
M
.
ratio
geometry