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Find sin A if sqrt(2) OI = AB - AC

Source: Chinese Mathematical Olympiad 1998 Problem 1

August 22, 2013
geometryincentertrigonometrygeometry unsolved

Problem Statement

Let ABCABC be a non-obtuse triangle satisfying AB>ACAB>AC and ∠B=45∘\angle B=45^{\circ}. The circumcentre OO and incentre II of triangle ABCABC are such that 2 OI=AB−AC\sqrt{2}\ OI=AB-AC. Find the value of sin⁡A\sin A.
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