By you

Let $M$ be the midpoint of side $BC$ of triangle $ABC$ . Let the median $AM$ intersect the incircle of $ABC$ at $K$ and $L, K$ being nearer to $A$ than $L$ , where $AK=KL=LM$ . If the ratio of the sides of triangle $ABC$ are in ratio $x:y:z$ . Find $x+y+z$ .