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Brazil National Olympiad
2004 Brazil National Olympiad
1
1
Part of
2004 Brazil National Olympiad
Problems
(1)
Prove that ABCD is a rhombus
Source: Brazilian M.O. 2004
10/17/2004
Let
A
B
C
D
ABCD
A
BC
D
be a convex quadrilateral. Prove that the incircles of the triangles
A
B
C
ABC
A
BC
,
B
C
D
BCD
BC
D
,
C
D
A
CDA
C
D
A
and
D
A
B
DAB
D
A
B
have a point in common if, and only if,
A
B
C
D
ABCD
A
BC
D
is a rhombus.
geometry
rhombus
conics
hyperbola
symmetry
inradius
incenter