Online Geometry Problem 790: Right Triangle, Altitude, Angle Bisector, Incircle, Tangency Point, Inradius, Circles, Tangent
Line, Congruence. Level: High School,
SAT Prep, College,
Mathematics Education

The figure below shows a right triangle ABC
with the incenter I, the inradius r, the altitude BH and the bisector BD of the angle HBC.
I_{1} is the incenter of the triangle AHB and I_{2} is the incenter of
triangle BHC. Prove that
.