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Gergonne's Theorem
The
incircle
of triangle
A
B
C
ABC
A
B
C
touches the side
B
C
,
A
C
BC, AC
B
C
,
A
C
and
A
B
AB
A
B
at
D
,
E
D, E
D
,
E
and
F
F
F
.
Then the lines
A
E
,
B
F
AE, BF
A
E
,
B
F
and
C
G
CG
C
G
are concurrent.
Their meeting point is called the
Gergonne point
.