Online Geometry Problems

Online Geometry Problem 792: Right Triangle, Altitude, Angle Bisector, Three Incircles, Incenters, Five Concyclic Points, Circles. Level: High School, SAT Prep, College, Mathematics Education

The figure below shows a right triangle ABC with the incenter I and the altitude BH. BD and BE are bisectors of angles HBC and ABH, respectively. I1 is the incenter of the triangle AHB and I2 is the incenter of triangle BHC. Prove that the points E, I1, I, I2, and D are concyclic.
 

Right Triangle, Altitude, Bisector, Incenters, Concyclic
 


 

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