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German National Olympiad
2012 German National Olympiad
5
5
Part of
2012 German National Olympiad
Problems
(1)
inradius of tetrahedron, inequality with lengths of nonadjacent edges
Source: Germany MO 2012 - 511345
10/30/2021
Let
a
,
b
a,b
a
,
b
be the lengths of two nonadjacent edges of a tetrahedron with inradius
r
r
r
. Prove that
r
<
a
b
2
(
a
+
b
)
.
r<\frac{ab}{2(a+b)}.
r
<
2
(
a
+
b
)
ab
.
geometry
inradius
3D geometry
tetrahedron
inequalities
geometric inequality