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Contests
National and Regional Contests
Germany Contests
German National Olympiad
2020 German National Olympiad
6
6
Part of
2020 German National Olympiad
Problems
(1)
Contact points of insphere and exsphere in tetrahedron are conjugate
Source: Germany 2020, Problem 6
6/22/2020
The insphere and the exsphere opposite to the vertex
D
D
D
of a (not necessarily regular) tetrahedron
A
B
C
D
ABCD
A
BC
D
touch the face
A
B
C
ABC
A
BC
in the points
X
X
X
and
Y
Y
Y
, respectively. Show that
∡
X
A
B
=
∡
C
A
Y
\measuredangle XAB=\measuredangle CAY
∡
X
A
B
=
∡
C
A
Y
.
geometry
3D geometry
tetrahedron
geometry proposed
Isogonal conjugate