Online Geometry
Problem 23: Right Triangle, Altitude, Circle, Incircles,
Inradius.
Level: High School, Honors Geometry, College,
Mathematics Education

In triangle ABC,
angle B is a right angle. BD is the altitude,
r, r1,
and r2, are the inradii of the triangles ABC,
ADB, and
BDC
respectively. Prove that r + r1
+ r2
= BD.