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Putnam
2017 Putnam
B1
B1
Part of
2017 Putnam
Problems
(1)
Putnam 2017 B1
Source:
12/3/2017
Let
L
1
L_1
L
1
and
L
2
L_2
L
2
be distinct lines in the plane. Prove that
L
1
L_1
L
1
and
L
2
L_2
L
2
intersect if and only if, for every real number
λ
≠
0
\lambda\ne 0
λ
=
0
and every point
P
P
P
not on
L
1
L_1
L
1
or
L
2
,
L_2,
L
2
,
there exist points
A
1
A_1
A
1
on
L
1
L_1
L
1
and
A
2
A_2
A
2
on
L
2
L_2
L
2
such that
P
A
2
→
=
λ
P
A
1
→
.
\overrightarrow{PA_2}=\lambda\overrightarrow{PA_1}.
P
A
2
=
λ
P
A
1
.
Putnam
Putnam 2017