# A Concurrency of Lines through Points of Tangency with Excircles

A Concurrency of Lines through Points of Tangency with Excircles

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

B

A

C

A

C

B

A

B

A

C

B

C

A'=AB⋂CA

C

C

B

B

B'=BC⋂AB

A

A

C

C

C'=CA⋂BC

B

B

A

A

A''=CA⋂AB

A

C

B

A

B''=AB⋂BC

B

A

C

B

C''=BC⋂CA

C

B

A

C