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Baltic Way
2011 Baltic Way
14
14
Part of
2011 Baltic Way
Problems
(1)
CH is parallel to AB
Source: Baltic Way 2011
11/6/2011
The incircle of a triangle
A
B
C
ABC
A
BC
touches the sides
B
C
,
C
A
,
A
B
BC,CA,AB
BC
,
C
A
,
A
B
at
D
,
E
,
F
D,E,F
D
,
E
,
F
, respectively. Let
G
G
G
be a point on the incircle such that
F
G
FG
FG
is a diameter. The lines
E
G
EG
EG
and
F
D
FD
F
D
intersect at
H
H
H
. Prove that
C
H
∥
A
B
CH\parallel AB
C
H
∥
A
B
.
geometry
circumcircle
geometry proposed