A Concurrency of Lines through Points of Tangency with Excircles

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A

B

C

A

B

A

C

B

A

B

C

A

C

A''

B''

C''

A'

B'

C'

H

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

C

⋂A

B

A

,

B''=A

B

A

⋂B

C

B

, and

C''=B

C

B

⋂C

A

C

. Then AA', BB', and CC' as well as AA'', BB'', and CC'' meet at H.