# Parallel Bisection

Geometry Level 2

In triangle $$ABC$$, the perpendiculars from $$A$$ to the internal bisectors of $$\angle CBA$$ and $$\angle BCA$$ meet those bisectors at $$X$$ and $$Y$$. Then which of the following options is correct : 

A :$$XY$$ is parallel to $$BC$$ and $$XY\sin B \sin C = BC \sin A$$ B :$$XY$$ is parallel to $$BC$$ and $$BC\sin B \sin C = XY \sin A$$ C :$$XY$$ is parallel to $$BC$$ and BY = CX D :$$XY$$ is parallel to $$BC$$

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