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Balkan MO
1986 Balkan MO
1
1
Part of
1986 Balkan MO
Problems
(1)
a line passing through the incenter
Source: bmo 1986
4/23/2007
A line passing through the incenter
I
I
I
of the triangle
A
B
C
ABC
A
BC
intersect its incircle at
D
D
D
and
E
E
E
and its circumcircle at
F
F
F
and
G
G
G
, in such a way that the point
D
D
D
lies between
I
I
I
and
F
F
F
. Prove that:
D
F
⋅
E
G
≥
r
2
DF \cdot EG \geq r^{2}
D
F
⋅
EG
≥
r
2
.
geometry
incenter
circumcircle
geometry proposed