HMMT 1999 O5

Let $r$ be the radius of the inscribed circle of triangle $A B C$. Take a point $D$ on side $B C$, and let $r_{1}$ and $r_{2}$ be the inradii of triangles $A B D$ and $A C D$. Prove that $r, r_{1}$, and $r_{2}$ can always be the side lengths of a triangle.