Play with triangle

Geometry Level 4

If the bisector of the angle A of triangle ABC meets BC in D, then \(a\) = \((b+c){[1-\frac{{AD}^{x}}{bc}]}^{y}\) where \(a\), \(b\) & \(c\) are the length of sides opposite to angle A, B & C respectively and \(x\) & \(y\) are rational numbers. Find the value \(xy\).

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