Mixtilinear Incircles

A

B

C

A'

B'

C'

A mixtilinear incircle is a circle that is tangent to two sides of a triangle and internally tangent to the triangle's circumcircle.

In the triangle ABC, suppose the three mixtilinear incircles touch the circumcircle at the points A', B', and C'. Then AA', BB', and CC' are concurrent.