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Math Prize For Girls Problems
2016 Math Prize for Girls Problems
19
19
Part of
2016 Math Prize for Girls Problems
Problems
(1)
Math Prize 2016 Problem 19
Source:
9/12/2016
In the coordinate plane, consider points
A
=
(
0
,
0
)
A = (0, 0)
A
=
(
0
,
0
)
,
B
=
(
11
,
0
)
B = (11, 0)
B
=
(
11
,
0
)
, and
C
=
(
18
,
0
)
C = (18, 0)
C
=
(
18
,
0
)
. Line
ℓ
A
\ell_A
ℓ
A
has slope 1 and passes through
A
A
A
. Line
ℓ
B
\ell_B
ℓ
B
is vertical and passes through
B
B
B
. Line
ℓ
C
\ell_C
ℓ
C
has slope
−
1
-1
−
1
and passes through
C
C
C
. The three lines
ℓ
A
\ell_A
ℓ
A
,
ℓ
B
\ell_B
ℓ
B
, and
ℓ
C
\ell_C
ℓ
C
begin rotating clockwise about points
A
A
A
,
B
B
B
, and
C
C
C
, respectively. They rotate at the same angular rate. At any given time, the three lines form a triangle. Determine the largest possible area of such a triangle.
Math Prize for Girls