IN-TST 2003 Problem 8

Let $ABC$ be a triangle, and let $r, r_1, r_2, r_3$ denoted its inradius and the exradii opposite the vertices $A,B,C$ , respectively. Suppose $a>r_1, b>r_2, c>r_3$ . Prove that (a) triangle $ABC$ is acute, (b) $a+b+c>r+r_1+r_2+r_3$ .