Find the maximum side

Geometry Level 4

Let \(I\) and \(O\) be the incenter and circumcenter of \(△ABC\) respectively.. ( \(△ABC \) is not an equilateral triangle ) And \( AIO^\circ \leq 90^\circ \) and \(AB=100cm,CA=102cm\)

Find the maximum possible value of side \(BC\)...

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