Online Geometry Problems

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.
 

Right triangle, Altitude, Angle Bisector, Inradius
 


 

Home | SearchGeometry | Problems | All Problems | Open Problems | Visual Index | 10 Problems | 781-790 | TrianglesRight Triangle | Circles | Tangent Line | Incircle | Angle Bisector | Altitude | Right triangle, Altitude and Incircle | Email | Solution / comment | By Antonio Gutierrez