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Portugal Contests
Portugal MO
2023 Portugal MO
4
4
Part of
2023 Portugal MO
Problems
(1)
area chasing starting with an equilateral
Source: 2023 Portugal p4 OPM
3/26/2024
Let
[
A
B
C
]
[ABC]
[
A
BC
]
be an equilateral triangle and
P
P
P
be a point on
A
C
AC
A
C
such that
P
C
‾
=
7
\overline{PC}= 7
PC
=
7
. The straight line that passes through
P
P
P
and is perpendicular to
A
C
AC
A
C
, intersects
C
B
CB
CB
at point
M
M
M
and intersects
A
B
AB
A
B
at point
Q
Q
Q
. The midpoint
N
N
N
of
[
M
Q
]
[MQ]
[
MQ
]
is such that
B
N
‾
=
14
\overline{BN} = 14
BN
=
14
. Determine the side of the triangle
[
A
B
C
]
[ABC]
[
A
BC
]
.
geometry
Equilateral
areas