Online Geometry Problems

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.

Right triangle, Altitude, Incircle, Circumcircle, Congruence
 


 

Home | SearchGeometry | Problems | All Problems | Open Problems | Visual Index | 10 Problems | 791-800 | TrianglesRight Triangle | Circles | Incircle | Circumcircle | Altitude | Right triangle, Altitude and Incircle | Congruence | Email | Solution / comment | By Antonio Gutierrez