Online Geometry Problems

Geometry Problem 789: Right Triangle, Altitude, Angle Bisector, Incircle, Tangency Point, Inradius, Circles, Tangent Line.

In triangle ABC, where angle B is a right angle, draw the altitude BH and the angle bisector BD of angle HBC. Let the incircle, with a radius of r, be tangent to side AC at point E. Our objective is to prove that DE is equal to r.

Right triangle, Altitude, Angle Bisector, Inradius
 

 Right angle triangle,
Altitude and bisector,
Incircle's sweet touch.
DE equals r, proof shines bright,
Geometry's elegant light.

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