A mixtilinear incircle is a circle that is tangent to two sides of a triangle and internally tangent to the triangle's circumcircle.[more]
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.[less]
The statement of the theorem is in "Notes on Euclidean Geometry" by Paul Yiu, p. 98.