# The Triangle problem

Geometry Level pending

A triangle $$ABC$$ has incenter $$I$$. Points $$X$$ and $$Y$$ are located on the line segment $$AB$$ and $$AC$$, respectively so that $$BX\cdot AB = IB^2$$ and $$CY \cdot AC = IC^2$$. Given that $$X,Y$$ and $$I$$ are collinear, find the possible value of the measure of angle $$A$$ in degrees.

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