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