CMO 1989 Problem 4

Given a triangle $ABC$ , points $D,E,F$ lie on sides $BC,CA,AB$ respectively. Moreover, the radii of incircles of $\triangle AEF, \triangle BFD, \triangle CDE$ are equal to $r$ . Denote by $r_0$ and $R$ the radii of incircles of $\triangle DEF$ and $\triangle ABC$ respectively. Prove that $r+r_0=R$ .