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1974 Poland - Second Round
3
3
Part of
1974 Poland - Second Round
Problems
(1)
coplanar projections of a vertex of tetrahedron on angle bisectors
Source: Polish MO Second Round 1974 p3
9/8/2024
Prove that the orthogonal projections of the vertex
D
D
D
of the tetrahedron
A
B
C
D
ABCD
A
BC
D
onto the bisectors of the internal and external dihedral angles at the edges
A
B
‾
\overline{AB}
A
B
,
B
C
‾
\overline{BC}
BC
and
C
A
‾
\overline{CA}
C
A
belong to one plane .
geometry
3D geometry
tetrahedron
angle bisector