MathDB
Problems
Contests
National and Regional Contests
Poland Contests
Poland - Second Round
1996 Poland - Second Round
6
6
Part of
1996 Poland - Second Round
Problems
(1)
1/2 \sqrt{a^2 +b^2 +c^2} is max distance in interior point of parallelepiped
Source: Polish second round 1996 p6
1/19/2020
Prove that every interior point of a parallelepiped with edges
a
,
b
,
c
a,b,c
a
,
b
,
c
is on the distance at most
1
2
a
2
+
b
2
+
c
2
\frac12 \sqrt{a^2 +b^2 +c^2}
2
1
a
2
+
b
2
+
c
2
from some vertex of the parallelepiped.
parallelepiped
distance
3D geometry
geometry