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Cono Sur Olympiad
2016 Cono Sur Olympiad
5
5
Part of
2016 Cono Sur Olympiad
Problems
(1)
Incenter and excenter
Source: Cono Sur Olympiad 2016, problem 5
8/28/2017
Let
A
B
C
ABC
A
BC
be a triangle inscribed on a circle with center
O
O
O
. Let
D
D
D
and
E
E
E
be points on the sides
A
B
AB
A
B
and
B
C
BC
BC
,respectively, such that
A
D
=
D
E
=
E
C
AD = DE = EC
A
D
=
D
E
=
EC
. Let
X
X
X
be the intersection of the angle bisectors of
∠
A
D
E
\angle ADE
∠
A
D
E
and
∠
D
E
C
\angle DEC
∠
D
EC
. If
X
≠
O
X \neq O
X
=
O
, show that, the lines
O
X
OX
OX
and
D
E
DE
D
E
are perpendicular.
geometry
cono sur
incenter