Online Geometry Problem 794: Right Triangle, Altitude,
Three Incenters, Circumcircles, Incircle, Congruence. Level: High School,
SAT Prep, College,
Mathematics Education

The figure below shows a right triangle ABC
with the incenter I and the altitude BH. D and E are the incenters of
triangles AHB and BHC, respectively. Prove that the incircle of
triangle ABC and the circumcircles of triangles BDE and DEI are
congruent. See also:
Artwork Problem
794.