Problem

Source: Chinese Mathematical Olympiad 1998 Problem 1

Tags: geometry, incenter, trigonometry, geometry unsolved



Let $ABC$ be a non-obtuse triangle satisfying $AB>AC$ and $\angle B=45^{\circ}$. The circumcentre $O$ and incentre $I$ of triangle $ABC$ are such that $\sqrt{2}\ OI=AB-AC$. Find the value of $\sin A$.