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Poland Contests
Poland - Second Round
1995 Poland - Second Round
5
5
Part of
1995 Poland - Second Round
Problems
(1)
points of tangency of incircles to 4 edges in tetrahedron are concyclic
Source: Polish second round 1995 p5
1/19/2020
The incircles of the faces
A
B
C
ABC
A
BC
and
A
B
D
ABD
A
B
D
of a tetrahedron
A
B
C
D
ABCD
A
BC
D
are tangent to the edge
A
B
AB
A
B
in the same point. Prove that the points of tangency of these incircles to the edges
A
C
,
B
C
,
A
D
,
B
D
AC,BC,AD,BD
A
C
,
BC
,
A
D
,
B
D
are concyclic.
geometry
3D geometry
tetrahedron
Concyclic
incircle