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1972 IMO Shortlist
5
5
Part of
1972 IMO Shortlist
Problems
(1)
Altitudes of a tetrahedron intersect if and only if
Source:
9/22/2010
Prove the following assertion: The four altitudes of a tetrahedron
A
B
C
D
ABCD
A
BC
D
intersect in a point if and only if
A
B
2
+
C
D
2
=
B
C
2
+
A
D
2
=
C
A
2
+
B
D
2
.
AB^2 + CD^2 = BC^2 + AD^2 = CA^2 + BD^2.
A
B
2
+
C
D
2
=
B
C
2
+
A
D
2
=
C
A
2
+
B
D
2
.
geometry
3D geometry
tetrahedron
altitudes
IMO Shortlist