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'=⋂
A
C
B
C
C
B
A
B
B'=⋂
B
A
C
A
A
C
B
C
C'=⋂
C
B
A
B
B
A
C
A
A''=⋂
C
A
A
C
A
B
B
A
B''=⋂
A
B
B
A
B
C
C
B
C''=⋂
B
C
C
B
C
A
A
C