SELECTION and TRAINING SESSION

Points $K$, $L$, $M$ lie on the sides $BC$, $CA$, $AB$ of a triangle $ABC$, respectively, so that $AK$, $BL$, $CM$ meet at a common point. Let $r_1$, $r_2$, $r_3$, $r$ be the inradii of the triangles $ALM$, $BMK$, $CKL$, $ABC$, respectively. Prove that $r_1+r_2+r_3\ge r$ or $r_2+r_3\ge r$ or $r_1\ge r$.