IGO 2017 A1

In triangle $ABC$ , the incircle, with center $I$ , touches the sides $BC$ at point $D$ . Line $DI$ meets $AC$ at $X$ . The tangent line from $X$ to the incircle (different from $AC$ ) intersects $AB$ at $Y$ . If $YI$ and $BC$ intersect at point $Z$ , prove that $AB=BZ$ .

Proposed by Hooman Fattahimoghaddam