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2015 BMT Spring
7
BMT 2015 Spring - Geometry 7
BMT 2015 Spring - Geometry 7
Source:
December 30, 2021
geometry
Problem Statement
Define
A
=
(
1
,
0
,
0
)
A = (1, 0, 0)
A
=
(
1
,
0
,
0
)
,
B
=
(
0
,
1
,
0
)
B = (0, 1, 0)
B
=
(
0
,
1
,
0
)
, and
P
P
P
as the set of all points
(
x
,
y
,
z
)
(x, y, z)
(
x
,
y
,
z
)
such that
x
+
y
+
z
=
0
x+y+z = 0
x
+
y
+
z
=
0
. Let
P
P
P
be the point on
P
P
P
such that
d
=
A
P
+
P
B
d = AP + P B
d
=
A
P
+
PB
is minimized. Find
d
2
d^2
d
2
.
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