Problem

Source: 4th Iranian Geometry Olympiad (Advanced) P1

Tags: geometry, Iran, IGO



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