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Polish MO Finals
1964 Polish MO Finals
3
3
Part of
1964 Polish MO Finals
Problems
(1)
coplanar touchpoints of tetrahedron and sphere
Source: Polish MO Finals 1964 p3
8/30/2024
Given a tetrahedron
A
B
C
D
ABCD
A
BC
D
whose edges
A
B
,
B
C
,
C
D
,
D
A
AB, BC, CD, DA
A
B
,
BC
,
C
D
,
D
A
are tangent to a certain sphere. Prove that the points of tangency lie in the same plane.
geometry
3D geometry
tetrahedron
sphere