Circle and triangle

Geometry Level 5

Above shows a triangle \(XYZ\) with \(XY= 18, YZ=16, XZ=14\). The bisector of angle \(X\) meets the straight line \(YZ\) at point \(W\).

The circle passing through point \(X\) and touching \(YZ\) at \(W\) cuts \(XY\) and \(XZ\) at points \(M \) and \(N\) respectively.

Find the distance \(MN\).

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