Online Geometry Problem 789: Right Triangle, Altitude, Angle Bisector,
Incircle, Tangency Point, Inradius, Circles, Tangent
Line. Level: High School,
SAT Prep, College,
Mathematics Education

The figure below shows a right triangle ABC
with the altitude BH and the bisector BD of the angle HBC. The incircle of
radius r is tangent to AC at E. Prove that DE = r.