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2019 MOAA
5
5
Part of
2019 MOAA
Problems
(1)
2019 MOAA Team P5
Source:
1/23/2022
Let
A
B
C
ABC
A
BC
be a triangle with
A
B
=
A
C
=
10
AB = AC = 10
A
B
=
A
C
=
10
and
B
C
=
12
BC = 12
BC
=
12
. Define
ℓ
A
\ell_A
ℓ
A
as the line through
A
A
A
perpendicular to
A
B
‾
\overline{AB}
A
B
. Similarly,
ℓ
B
\ell_B
ℓ
B
is the line through
B
B
B
perpendicular to
B
C
‾
\overline{BC}
BC
and
ℓ
C
\ell_C
ℓ
C
is the line through
C
C
C
perpendicular to
C
A
‾
\overline{CA}
C
A
. These three lines
ℓ
A
,
ℓ
B
,
ℓ
C
\ell_A, \ell_B, \ell_C
ℓ
A
,
ℓ
B
,
ℓ
C
form a triangle with perimeter
m
/
n
m/n
m
/
n
for relatively prime positive integers
m
m
m
and
n
n
n
. Find
m
+
n
m + n
m
+
n
.
geometry
team
2019