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Putnam
1947 Putnam
B6
B6
Part of
1947 Putnam
Problems
(1)
Putnam 1947 B6
Source: Putnam 1947
4/3/2022
Let
O
X
,
O
Y
,
O
Z
OX, OY, OZ
OX
,
O
Y
,
OZ
be mutually orthogonal lines in space. Let
C
C
C
be a fixed point on
O
Z
OZ
OZ
and
U
,
V
U,V
U
,
V
variable points on
O
X
,
O
Y
,
OX, OY,
OX
,
O
Y
,
respectively. Find the locus of a point
P
P
P
such that
P
U
,
P
V
,
P
C
PU, PV, PC
P
U
,
P
V
,
PC
are mutually orthogonal.
Putnam
3D geometry
orthogonal