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Putnam
1960 Putnam
A4
A4
Part of
1960 Putnam
Problems
(1)
Putnam 1960 A4
Source: Putnam 1960
6/11/2022
Given two points,
P
P
P
and
Q
Q
Q
, on the same side of a line
L
L
L
, the problem is to find a third point
R
R
R
so that
P
R
+
R
Q
+
R
S
PR+ RQ+RS
PR
+
RQ
+
RS
is minimal, where
S
S
S
is the unique point on
L
L
L
such that
R
S
RS
RS
is perpendicular to
L
.
L.
L
.
Consider all cases.
Putnam
geometry
Locus