olymmath

CMO 1998 Problem 1

  • Day 1

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 .

Dataset text AI-MO AoPS. Quoted with source.

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