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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