iPad Apps: Apollonius Software. Problem 794: Right Triangle, Altitude, Three Incenters, Circumcircles, Incircle, Congruence. Level: High School, SAT Prep, College, Mathematics Education. Level: High School, College.

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.

Apollonius iPad Apps: Right triangle rectangle, ALtitude, Incenter, congruence

Apollonius for iPad: Problem 794, Right Triangle
I drew the geometric construction above using Apollonius for iPad.

Apollonius is an interactive geometry app (IGS, or Dynamic Geometry Environment, DGE). It allows you to create geometric constructions, such as those that can be made using a ruler and a compass, and subsequently move parts of your constructions to explore the relationship between the geometric objects on the screen.

Apollonius is inspired by software such as GeoGebra, The Geometer's Sketchpad and Cabri, but its interface is especially designed for touch screen.