WOLFRAM|DEMONSTRATIONS PROJECT

A Concurrency of Lines through Points of Tangency with Excircles

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Let ABC be a triangle with orthocenter H. Let
B
A
be the point of tangency of CA with the excircle opposite A, and similarly define
C
A
,
C
B
,
A
B
,
A
C
, and
B
C
. Let
A'=
A
C
B
C
⋂
C
B
A
B
,
B'=
B
A
C
A
⋂
A
C
B
C
, and
C'=
C
B
A
B
⋂
B
A
C
A
. Let
A''=
C
A
A
C
⋂
A
B
B
A
,
B''=
A
B
B
A
⋂
B
C
C
B
, and
C''=
B
C
C
B
⋂
C
A
A
C
. Then AA', BB', and CC' as well as AA'', BB'', and CC'' meet at H.